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HP-16C Emulator Manual

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1. Remember that executing a function directly via XEQ or assigned to a key does not store the function s id in the LASTF buffer so even if you can access the LASTF functionallity the buffer contents will only be updated when you use 16C or other launcher to execute the function Both the 16C prefix Keyboard and the 16KEYS approach use the same 16C overlay shown in page 15 of this manual Since both are available on the emulator you can choose the one that suits you better the choice is yours c Martin McClure Page 40 of 63 September 2015 HP16C Emulator Module for the HP 41CX 4 2 A few development aids The remaining section of the manual describes a handful of utility functions that were using during the development of the module for testing purposes Some may be of interest to you if you feel adventurous and decide to explore the 16C Buffer or other more technical aspect of the implementation 4 2 1 FX Buffer registers handling A2FX CLRFX EX2FX FX2EX FXSZ As the repository of the digits shown in the displaying of the results the buffer FX registers have a pivotal role in the emulator design Normally you won t have to worry about their contents which will be updated by the module s functions and accessed by SHOW and WINDOW but should you feel intrigued here are the functions available for the tasks Note that the output of these functions is does not utilize the module s digi
2. Me then allen Note remember that the sigma character in a sub function name cannot be directly entered via the key SHIFT F in ALPHA mode thus you need to use the N character i e for NDGT instead c Martin McClure Page 43 of 63 September 2015 HP16C Emulator Module for the HP 41CX 4 2 5 Test for Maximum Negative signed Value MNV e MNV is a test function to check whether the number in 16X is the Maximum Negative signed Value MNV for the currently selected word size The result will be YES NO skipping a program line if false as with any standard tests Of all the conventions used on the 16C calculator one of the trickiest to grasp is that of the maximum negative value for signed complements Even if the definition is clear enough some of the particular function results when the operand is such a maximum negative value may be unexpected or even disconcerting to the untrained eye and it accounts for many numerous singularities in the general algorithms to properly emulate the real machine For starters this is the only value that equals its own 16CHS in 2CMP This is not the only remarkable thing about it but remember this one we ll use it later on We define the maximum negative value as the largest absolute number with a negative sign i e the msb is set in either 1CMP or 2CMP Given the arrangment of the negative values see appendix 1B the maximum negative happens
3. Bit Reversal function Often it s needed to reverse the bit sequence of a word be that because of incompatible data transfer protocol conventions or for another legit reason This is no surprisingly the subject of applied math and sophisticated algorithms exist but this implementation follows a sequential alteration of the bits to build a mirror image of the initial word Note that the reversion is made on the complete word size i e taking into account the leading zeros as well There are two ways to circumvent that if not desired 1 Execute WSFIT first to adjust the word size to the number of relevant bits then call REV Realize that the word size has been changed and may need changing back 2 Call REV and then use RJY on the result to get rid of those reversed leading zeros after they re reversed into the LSB positions Example set ws 12 HEX mode Get the bit reversal of 9 16NPT 9 gt H 9 orb 00001001 REV gt H 90 or b 10010000 RJY gt H 9 since 0x9 is a polindrome value so to speak Example Verify that the bit reversal of 0xD9 with a word size ws 8 is 0x9B Which is easy enough to check in binary base but pretty challenging in decimal with 2 s complement set aS a manner of example 3 4 4 Right and Left Justification There is no Right Justify function on the original 16C but somehow it felt just natural to include that function to complete the set if only for symmet
4. LBL 00 size is in the 16X register lines 3 amp 4 11 RCL 1 11 16RCL In fact here we use an insider s trick 12 B 12 128 using just the real X register only valid 13 13 BITS for 16WSZE 14 X lt gt Y 14 16 15 0 15 16X lt gt Y Sub functions in brown color really use 16 RLC 16 0 the 16C launcher followed by an index 17 17 16LOW number 18 X lt gt Y 18 RLC 19 DSZ 19 16 Entering 16C values requires either 16NPT or LOW16 for numbers below 20 GTOO 20 16X lt gt Y ks 32 bits This is how zero was input in 21 RTN 21 DSZ lines 16 and 17 22 GTOOO 23 SHOW DSZ operates on standard values as an 24 END index very much like ISG and DSE do A final SHOW instruction has been added to see the 16C result Note how all the stack lift and drop are performed in exactly the same way as in the original machine pretty much following the same rules as in all RPN designs c Martin McClure Page 50 of 63 September 2015 HP16C Emulator Module for the HP 41CX Appendix B2 Square Root using Newton s Method The program below is an alternate and very slow way to calculate the square root of a number simply using an iterative approach following Newton s method _ A l 2 Finding VS is the same as solving the equation f z 5 1 Therefore any general numerical root finding algorithm can be used Newton s method for example reduces in this case to the so called Babylonian method B fl
5. and displays the result Addition Subtraction Routines Addition and subtraction may be much simpler functions but the complication for these functions comes from the complement modes and their influence on the carry flag status overflow flag status and adjustment of the final answer One routine handles both 16 and 16 it uses an internal system flag specifically system flag 9 to perform the unique code for the specific function Here is the addition subtraction function in detail 1 16LastX is performed to save the value of buffer 13 and stack register X into buffer 14 and stack register L 2 The result of buffer 12 added subtracted from buffer E1 replaces E1 The result of the binary value of Y added subtracted from buffer EO replaces E0 Carry borrow from EO propagates to E1 carry from E1 is left in E1 3 If 1 s complement mode a special internal flag specifically flag 6 is set to show we may have to bump the result 4 A special carry and overflow flag set routine is called to determine which flags to set This is described in more detail below 5 An extended stack drop is performed and buffer E1 replaces buffer 13 and BCD of buffer EO replaces register X 6 The addition subtraction routine returns via a routine that translates the values in buffers EO E1 into buffers FO thru F7 and displays the result The routine that handles carry and overflow or out of range flags uses the following algorithms Assume that
6. 1 1 33 8 589 934 591 2 3 34 17 179 869 183 3 7 35 34 359 738 367 4 15 36 68 719 476 735 5 31 37 137 438 953 471 6 63 38 274 877 906 943 7 127 39 549 755 813 887 8 255 40 1 099 511 627 775 9 511 41 2 199 023 255 551 10 1 023 42 4 398 046 511 103 11 2 047 43 8 796 093 022 207 12 4 095 44 17 592 186 044 415 13 8 191 45 35 184 372 088 831 14 16 383 46 70 368 744 177 663 15 32 767 47 140 737 488 355 327 16 65 535 48 281 474 976 710 655 17 131 071 49 562 949 953 421 311 18 262 143 50 1 125 899 906 842 620 19 524 287 51 2 251 799 813 685 250 20 1 048 575 52 4 503 599 627 370 490 21 2 097 151 53 9 007 199 254 740 990 22 4 194 303 54 18 014 398 509 481 983 23 8 388 607 55 i 36 028 797 018 963 967 24 16 777 215 56 il 72 057 594 037 927 935 25 33 554 431 57 g 144 115 188 075 855 871 26 67 108 863 58 i 288 230 376 151 711 743 27 134 217 727 59 g 576 460 752 303 423 487 28 268 435 455 60 g 1 152 921 504 606 846 975 29 536 870 911 61 7 2 305 843 009 213 693 951 30 1 073 741 823 62 if 4 611 686 018 427 387 903 31 2 147 483 647 63 g 9 223 372 036 854 775 807 32 4 294 967 295 64 18 446 744 073 709 551 615 Also shown in the graphic below using a logarithm scale c Martin McClure Page 47 of 63 September 2015 HP16C Emulator Module for the HP 41CX Appendix A2 The Hexadecimal Number System The base of this number system is 16 d The numbers 0 9 as well as the letters A to F are used to represent 11 d to 15 d The carry over O 0
7. 9 16X lt 0 tests 16X less or equal to 0 value in 16X YES NO skips line if false 10 16X gt 0 tests 16X greater than zero value in 16X YES NO skips line if false 11 16X gt 0 tests 16X greater or equal 0 value in 16X YES NO skips line if false 12 16X Y tests 16X equal to 16T values in 16X and 16Y YES NO skips line if false 13 16X Y tests 16X not equal to 16Y values in 16X and 16Y YES NO skips line if false 14 16X lt Y tests 16X less than 16Y values in 16X and 16Y YES NO skips line if false 15 16X lt Y tests 16X less equal to 16Y values in 16X and 16Y YES NO skips line if false 16 16X gt Y tests 16X greater than 16Y values in 16X and 16Y YES NO skips line if false 17 16X gt Y tests 16X great equal to 16Y values in 16X and 16Y YES NO skips line if false 18 16X44 enters 16X in all stack levels value in 16X 16X is replicated 19 DSZ Decrement and skip if Zero content of ROO data reg ROO decrements skip iz aero 20 GET16 Gets 16C buffer from X Mem X mem file name in ALPHA new 16C buffer is in place 21 ISZ Increment and skip if zero content of ROO data reg ROO increments skip iz aero 22 LOW16 Enters x into 16X register real number value in x new value in 16X 23 NAND Negative AND values in 16X and 16Y Result in 16X stack drops 24 NOR Negative OR values in 16X and 16Y Result in 16X stack drops 25 REV Reverses bits in word value in 16X result in 16X argument to 16L 26 RJY Right Justifies the value value in 16X Result in 16X pos
8. FX regs to the EX regs Shows number of non zero chrs in FX Hex to Decimal Copies the Low bits into the High bits Moves the Low bits to the High bits Swaps Low and High 16X bits Shows Leading Zeros Test for Maximum Negative Value Toggles Silent Loud Mode Shows maximum value for ws Appends chr X to laft Alpha Shows Copyright Message value in 16X String in ALPHA none none none Value in X reg Value in 16X Value in X reg Value in 16X Binary Data in EX regs Chars Data in FX regs none Hex String in Alpha Data in 16X Data in 16X Data in 16X Data in 16X Value in 16X none ws data in buffer Crh value in X none result in 16X argument to 16L Chars transferred to FX regs Base value in 16X 16C Buffer in Memory FX regs cleared reset Hex string in Alpha Shows sum and enters it Digits left Justified Reversed digits in 16X Chars written in FX Regs Binary Data in EX regs Number of characters in X Result in X register Copies X to b13 Moved X to b13 X reg and b13 swapped Leading Zeros added YES NO skips line if false Active mode toggled shows value in x Appended to left Alpha Shows message If you re familiar with the 16C calculator you ll no doubt recognize the majority of functions in the main FAT as such as been the criteria for function FAT allocation Their functionality and operation should be pretty much identical to their original counterparts but there are a few differences that will be c
9. L H MNV NAND NOR REV RIY SAVE16 SLN SRN _ TS L WSFIT WSMAX x 0 K Y _ K LA XNOR c c Martin McClure Page 10 of 63 September 2015 HP16C Emulator Module for the HP 41CX c bE IHTH STRUCTURE 2 1 The Martin McClure Buffer Without doubt the 16C Buffer is the cornerstone of the 16C Emulator module Designed to fulfill the storage requirements for 64 bit data values and provide available scratch registers for data management and auxiliary calculations this buffer is automatically created and maintained by the calculator behind the scenes all transparent to the user Even if you can use the module completely unaware of the 16C buffer knowing the fundamentals on its structure and operation will largely increase you understanding of the module significantly smoothing the learning curve Those wanting to know more should refer to appendix B for a more detailed description of the buffer registers and design Data Size and Registers the problem at hand Because the data values can be as large as 64 bit the 56 bit standard 41C registers are not sufficient to hold the values in all cases even if we were to use up all of them in a custom data format The solution implemented uses two standard hp 41 registers for each 16C value with each register holding 32 bits worth of information We ll call those registers the lower bits and the higher bits registers This is so regardless of the s
10. as to the ringing of the words but under no circumstance denotes any priority in the order of the names c Martin McClure Page 6 of 63 September 2015 HP16C Emulator Module for the HP 41CX Function index at a glance Without further ado here are all 125 functions included in the main and auxiliary FATs Function Description Input Result 1 HP 16C Shows Library 4 Splash none Flashes splash msg 2 16C _ Main 16C Keyboard Launcher see 16C keyboard overlay 2xecutes function 3 164 ___ WEX Subfunction by index Prompts for index executes function 4 16S _ XEQ sub function by Name Prompts for name executes function 5 16 Integer mode addition values in 16X and 16Y Result in 16X stack drops 6 16 Integer mode subtraction values in 16X and 16Y Result in 16X stack drops 7 16 Integer mode multiplication values in 16X and 16Y Result in 16X stack drops 8 16 Integer mode Division values in 16X and 16Y Result in 16X stack drops 9 16SQRT Square Root value in 16X result in 16X argument to 16L 10 16WSZ __ Sets Word Size prompts for word size flashes size on LCD 11 1CMP Sets 1 s Complement Mode none changes mode sets flag 1 12 2CMP Sets 2 s Complement mode none changes mode sets flag 2 13 AND Logical Intersection values in 16X and 16Y Result in 16X stack drops 14 ASR Arihtmetic Shift Right value in 16X result in 16X argument to 16L 15 b _ Bit Set testing value in 16X bit in prompt YES NO skips line if false 16 BINM
11. as well as during a single step execution in a program This provides visual feedback to the user as to whether the function was that intended to use by direct enumeration using FCAT hitting when the sub function name is shown and the enumeration is paused single stepped In terms of the 16C keyboard you can access 16 pressing PRGM and 16 pressing ALPHA keys respectively at the 16C prompt and some other launchers as well all conveniently layed out for you Note Even if the sigma character can be typed during the 16 prompt it however won t be recognized by the name search routines due to some conflicts in the character value assignment You need to use the N character instead or the 16 function followed by the sub function index This only impacts the sub function DGD and the three sub function launchers covered before c Martin McClure Page 33 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 3 1 Last Function functionallity and Programability Also common to the other modules not surprisingly since the same routines in the Library 4 are used the function is either executed in manual mode or automagically entered as two program lines in PROGRAM mode Furthermore the subfunction code is stored in the LastFunction buffer so it can be re executed pressing LASTF on the 16C keyboard Radix key at the 16C_ prompt Note that 16 can also be used to execute functions in the ma
12. for the most dramatic changes in utilization since on the 41 the 16C Emulator is just one of the many other modules that can be used simultaneously and it needs to co exist with the 41 native OS But far from being a disadvantage that makes it much more interesting as you benefit from the power and capability offered on the 41 like extendend capacity in data registers and program space larger LCD with automatic scrolling functionality and of course the ability to compbine the 16C functions with any other from the 41 OS at the same time Is it a better 16C than the original 16C Well that depends on your previous experience and bias so if you live and breathe by the original machine this module will make you do things a little different but if you re just a casual user or start anew the 16C Emulator module on the 41 is a much more convenient tool with a more sophisticated user interface and rounder function set not lacking any functionality from the original machine Automated Base Conversions the four modes There are five base modes on the 16C Emulator Binary Octal Decimal Hexadecimal and Floating Point By default the floating point mode is pre selected upon initialization i e the first time the calculator is started with the 16C Module plugged in There will be no value displayed while the machine is in FLOAT mode The number conversion between the different bases is performed automatically as you select the base mode o
13. is multiplied by the partial quotient and subtracted from the dividend Occasionally this results in a negative value of the remaining dividend so the partial quotient is adjusted to allow a positive difference The final dividend after subtraction is used for the next partial division The length of the partial divisor and piece of dividend depends on the length of the full divisor For divisors less than up to 24 bits the full divisor is used and no multiply and subtraction adjustment is required Here is the division process in detail In actual code the process is divided into multiple sections based on divisor length and whether single or double dividend length 1 16LastX is performed to save the value of buffer 13 and stack register X into buffer 14 and stack register L 2 For 16 and RMD the binary value of Y and contents of buffer 12 dividend are moved to buffers E2 and E3 The binary value of X and buffer 13 divisor are already in EO and E1 3 For DBL and DBLR the binary value of Y and contents of buffer 12 high order dividend are moved to buffers FO and Fl The binary value of Z and contents of buffer 11 low order dividend are moved to buffers E2 and E3 The binary value of X and buffer 13 divisor are already in EO and E1 4 For DBL and DBLR the values in buffers FO and F1 need to be shifted down into buffers E2 and E3 depending on word size This allows the division process to basically be the same for all word
14. is then transferred to CPU F8 status which will be clear if zero or set if not zero This also allows for faster branching points in the code downstream RLRR RLRR RLRR RLRR RLRR This routine prepares a 1 mask located at the ws bit in the EO E1 register depending on the ws value IMWSPOS sd A177 284 CLRF 7 simple version A178 013 JNC 02 Mwsps jA179 288 SETF7 flag the AND action S AA 198 C M ALL C C 1 S amp X RAMSLCT READATA A C S amp X buffer header pointer to b00 select b00 b00 contents ws in A S amp X assumes ws lt 33 The mask is stored in B and the pointer to EO E1 is left in Con exit A181 021 CON 33 low bits limit f PA lt C S amp X is m lt 33 RLRR JC 04 yes gt LOWERB RLRR SETF 1 flag higher bits case RLRR A185 266 C C 1 S amp X 032 RLRR A A C S amp X count ws 32 RLRR LOWERB A187 04E C 0 ALL blank slate RLRR A188 C C 1 M put 0001 in C lt 3 gt digit RLRR INXTBIT Ma89 1A6 A A 1 S amp X decrease counter RLRR 346 PAHO S amp X RLRR 01B JNC 03 exitif all done RLRR 1FA C C C M shifts the 1 one bit left RLRR 3E3 JNC 04 do next RLRR mask Is 000 1 000 RLRR IWSRGPT _ _ s A18F 198 C M ALL buffer header A CS amp X_ putin A for math non gets pointer to reg with ws bit 30 LDI S amp X Al either EO E1 as per F1 0o08 ___ 8 ABOVE HEADER __ _____ location of bEO FSET 1 higher bits RLRR JNC 02 y o OOOO
15. may have noticed the conspicuous absence of the test conditional functions from the 16C overlay or almost since there above the key are to be found the two test launchers X Y and X 0 very much following the design used by other calculators like the HP 32S All individual test functions are in the auxiliary FAT thus they re implemented as sub functions In fact that s also the case for the X 0 launcher itself even if that fact is totally transparent to the user and on the overlay There are six different tests for XY conditions plus another six for zero conditions Each group is split into two screens with three choices on each of them as shown in the pictures below You can use the SHIFT key to move between the screen choices within each launcher and the anchor key to change the launcher type back and forth And pressing the anchor key A changes to the zero test groups In all cases the selection is made using the top row keys C D and E You can also hit the anchor key A to toggle between the X Y and X 0 launchers right from within them Being subfunctions adds no restriction to the testing functionality even if an index line number is required in a program to identify which one is to be used As it is known the non merged functions cannot be located after a test conditional or otherwise the skip if false rule will jump into the middle of both lines but there s nothin
16. performance considerations They are described in the following paragraphs c Martin McClure Page 13 of 63 September 2015 HP16C Emulator Module for the HP 41CX Maximum values will be observed Not only does 16NPT know which digits are allowed for the current base but it also imits the entry so the maximum value is not exceeded This however has an exception in decimal mode for word sizes of 34 and up where in some circumstances values slightly larger than the maximum can be keyed in They however will be normalized upon data entry completion by applying the current mask to the digits in ALPHA Examples in DEC mode and 2CMP select word size 34 and attempt to enter the following two values 8 589 934 595 and 8 589 934 999 Are the results what you had expected 16NPT 16NPT gt d 8 589 934 589 gt d 8 589 934 185 5 8 9 9 3 4 5 9 5 ENTER SPE o ie e e i oro 8 5 9 5 8 1 4 1 1 1 1 9 1 J ENTER A special way to terminate the digit entry is by pressing one of the four arithmetic keys for a direct chained operation or the key to directly enter the negative value of the number typed in This not only saves three keystrokes but also provides a convenient way to introduce negative numbers not worrying about the current complement mode Example enter the negative value of H 25 with a word size of 32 and 2 s complement 16NPT 2 5 gt H FFFFFFDB On the fly Base Rotation during I
17. range is needed the precedence sign bit is not necessary unsigned mode and the value range is used for all cases from 0 to 255 d assuming the same word size of 8 bits In the table below you can see the correspondence between the three sign modes for decimal numbers 0 15 represented in binary using a four bit word size 0 6 6 0110 8 9 1001 c Martin McClure Page 49 of 63 September 2015 HP16C Emulator Module for the HP 41CX Appendix B1 Programming Examples Let s see an example of how the 16C Emulator module functions are used in a program We ll use the Checksum Calculation example from the 16C manual pages 90 91 and 92 The program assumes you have pre loaded 4 bit hex values in registers R1 to R10 as follows The table below shows both the original program and the equivalent using the Emulator functions for a side to side comparison not surprisingly very similar in concept but with some differences especially in the 16C stack management Remarks hp 16c Program 16C Emulator Code 1 Indirect Register I corresponds to ROO 1 LBL D 1 LBL CHKS 2 UNSIGN 2 UCMP RCL i uses the indirect capability of 3 4 3 4 16RCL adding 128 to the 16C register 4 WSIZE 4 16WSZ number 5 HEX 5 HEXM l 6 g 6 10 Note the non merged arrangement in J STO J STO 00 dia nr 12 for al with the rg in a 7 XIE e next program line aaah Note how the parameter for the word 10 mka 10__
18. register c Martin McClure Page 27 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 8 A few Examples Gray Code Bit Extraction Add w Carry The following examples are taken from the HP 16C article published in the May 1983 HP Journal issue With them you should get familiar with the way the emulator functions are used to prepare 16C like programs on your HP 41 We re sure you ll appreciate having the function names shown as opposed to their keycodes on the original machine and enjoy seeing the goose flying a Binary to Gray and Gray to Binary conversions Note that the test function 16X 0 2 16ENT 8 16ENT Really corresponds to the combination of 3 SR 9 LBLO2 the two program lines 4 XOR 10 SR 5 SHOW 11 XOR 16 and 6 RTN 12 LAST16 7 13 16X 0 14 GTO 02 15 16RDN 16 SHOW 17 RTN Example convert b 11010 to Gray code and back to binary Keystrokes Result Comment BINM b XXXXX current 16X content 16NPT 1 1 0 1 0 R S b 11010 enters binary value in 16X XEQ GRAY b 10111 Gray equivalent XEQ BIN b 11010 Original value back b Bit Extraction and Addition with Carry Note the usage of 16NPT to enter values 2 16RDN 2 CF03 to the 16C register as shown in lines 3 RRN 3 a 7 8 of bXT and lines 3 4 of 16 C 4 16RUP 4 16NPT 5 LAST16X 5 RLC Note also the carry flag is 3 on the 6 16 6 16 emulator not 4 as in the original 7 p 7 CFOS machine 8 16NPT
19. size of the storage registers in the HP 41 is fixed always 56 bits whereas on the 16C it is a variable number defined by the smallest multiple of 4 bits half bytes equal to or greater than the current word size Depending on your programs and needs that may be a fundamental difference or just a negligible detail but nevertheless it is important to be aware of if for the cases where this becomes a relevant consideration Suffice it to say that the memory allocation is a very particular affair on the 16C much more intricate than on any other HP calculator to say the least c Martin McClure Page 26 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 7 Square Root and Square Power 16X42 The Square root function is a bit of a hybrid in that is uses the native OS routines to calculate the result This is clearly a way around approach that works just fine for input values lower than 2 33 but that needs to be adjusted for larger values of the input parameter The adjustment is done in a short FOCAL code stub triggered by the function itself when required It simply checks if the square power of the result matches the input parameter If it does then it s a perfect square that needs no adjustment If it doesn t then it may need subtracting one to the result and it will always have to set carry The only caveat to this approach is that the original input value is not left in the LST16X register but in the 1
20. the 41 OS the code occasionally uses subroutines from the CX OS code This was a compromise to enhance the functionality at the economy of ROM space as it avoided having to replicate large code streams already available on the CX Don t use this module on a plain 41C or CV machine it ll have surely unexpected and probably unwanted results The module checks for the presence of the dependencies i e the Library 4 and the CX If the Library 4 is missing or the machine is not a CX the errors will halt it to avoid likely problems Note also that this module is not compatible with pages 6 and 7 avoid plugging it in those locations Remember The HP16C Emulator module extensively uses routines and functions from the Page 4 Library Make sure the Library 4 revision O1 or higher is installed on your system or things can go south Refer to the Page 4 Library documentation to properly configure the Library 4 before use c Martin McClure Page 5 of 63 September 2015 HP16C Emulator Module for the HP 41CX Organization of this manual We have no intention to duplicate the HP 16C Computer Scientist Manual which is the best reference to learn about the functions and concepts behind this module This manual won t teach you the intricacies of the Carry and Out of Range flags or the binary concepts behind the 1 s or 2 s complement signed modes for instance You re encouraged to read the original 16C manual if needed It is howe
21. the display to help you interpret the results which believe me there will be differences depending on the current setting AS a consequence I need to use the STATUS function very frequently just to see the mode not very efficient in my mind On the 16C Emulator this is always shown by the first three user flag annunciators 0 1 and 2 At all times one of those three will be set to show you the current complement mode where zero means unsigned mode They act as semaphores more than programming flags and while you can manually changed them using the 41 SF CF functions it is strongly recommended you don t do so Some functions rely on their status during intermediate calculations and besides they ll be changed back by the 16C Emulator at the first opportunity to syncronize with the complement mode set In other words flags 0 1 and 2 are reserved as they are taken over by the 16C Emulator in ther role of signed unsiged mode semaphores The example below shows the decimal representation of H 9000 in 1CMP and 2CMP modes for a word wsize of 16 bits Can you tell at a glance which one is which do 28672 USER 2 Carry and Out of Range flags CY amp OOR The original machine uses flags 4 and 5 for the Carry and Out of Range conditions respectively The display shows C for Carry set and G for OOR set which therefore are matched to flag 4 and 5 On the 16C module however the flags used are 3 for Carr
22. the familiar DATA ERROR message c Martin McClure Page 23 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 4 Prompting Functions The HP 41 features a user interface design more advanced than what the original 16C has One of the nicer features is the prompting functions whereby the function s argument is entered at the prompt in manual mode Whenever possible we have favored this implementation over the usage of the 16X register for function parameter saving so keystrokes and simplifying the data entry sequence as this approach removes the need to use the fe keypad or 16NPT to enter the parameters This is only applicable to the operation in manual RUN mode In Program mode the functions behave in the same way they do on the original 16C machine The new prompting functions are shown in the table below Parameter Function Parameter MASKL__ itows RRN tows MASKRL 1tows RRN itow 1 RN litow SLN Function Cb ___ Otows t RLCN__ Atows 1 b ___ Otows 1 16WSZE__ 0 lt ws lt 65 SLN tows WINDOW_ O0 lt w lt 8 SRN o ff ttows Pt Common implementation features to all these functions are as follows Parameter entry requires two digits always assumed to be decimal numbers irrespective of the selected base mode You can use the soft keys on the two top rows for parameters 1 to 10 The prompts will stay put i e the function will
23. to W7 placed at the left of the LCD The selected base character is also shown the the right of the LCD in all cases When used in a program WINDOW will take the argument from the next program line as a non merged design similar to other prompting functions like 16STO and 16RCL The True Meaning of GRAD revealed If you always thought that it stood for a so called centesimal angular mode seldom used except by surveyors we re told then you re in for a nice revelation GRAD really stands for GReater than Alpha Display The GRAD annunciator will be lit when the value to display exceeds the 24 character limit of the ALPHA registers as a visual clue that you need to use WINDOW to see the complete value This will only occur in binary base mode with word sizes larger than 24 bits and when the significant bits exceed that number remember the leading zeroes won t be shown Every other case is well served by SHOW using the ALPHA register even if it is exercising its scrolling capacity c Martin McClure Page 17 of 63 September 2015 HP16C Emulator Module for the HP 41CX Let s see an example using a large word size say ws 56 Enter the decimal value 1234567789 and show it in binary using the WINDOW function screens Exceute BINM this sets GRAD and WINDOW Then use the hot keys to access all the relevant screens as follows Note the storage order of the bits with the MSB in the leftmost position of W
24. user interaction is required The buffer reserves one register for each of the four modules that have sub functions plus the header also stores the 41Z last function which is always in its main FAT Therefore up to five last functions can be simultaneously available at any given time A total of five registers are used as follows b4 SandMatrix fcn id SandMath fcn id PowerCL fcn id 16C Emulator Time based Seed RND o Header a Not bad for a single line 12 chars LCD machine from 1979 won t you agree Which once again proves the adagio t s not the size of the wand what matters but the skill of the wizard who uses it c Martin McClure Page 34 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 4 Individual Description of the new functions The remaining sections provide a succint description of the added functions not included in the original 16C calculator and not covered already in previous chapters of this manual Some are little embellishments of standard 16C functions or natural extensions of the same ideas that probably weren t included in the original machine due to space constraints They are located in the auxiliary FAT and therefore you need to use the 16 or 16 launchers to execute them 3 4 1 Negative Logic Functions and Not needing much as description these three round up the set of logical functions and save you from having to NOT the result of their po
25. w represents the word size in use 1 thru 64 Assume that the lowest bit of the result is bit 0 thus the highest bit of the result is n OV bit and for 1 s complement and 2 s complement the n 1th bit signifies positive or negative value CY bit Z X Y for addition or X Y for subtraction So we have three CY bits to consider XCY YCY and ZCY and one overflow bit ZOV For no complement mode the carry and overflow bits are set identically they represent the value of the ZOV bit For 1 s complement mode if CY is set then the result is bumped 1 for addition 1 for subtraction For 1 s and 2 s complement modes the algorithms are a Carry ZCY b OOR XCY xor YCY and not ZCY xor ZOV or not XCY xor YCY and ZCY xor ZOV c Martin McClure Page 60 of 63 September 2015 HP16C Emulator Module for the HP 41CX Creating a Carry Mask 1 at the WS position This routine prepares a 1 mask located at the ws bit in the E0 E1 register depending on the ws value The mask is stored in B and the pointer to E0 E1 is left in C on exit If the word size exceeds 32 the status of CPU F1 will be set as a marker for the following routines that the mask s 1 bit is in the bE1 register higher bits or conversely in the bEO lower bits if CPU F1 is clear Two entry points exist so CPU flag 7 controls whether the mask is also AND ed with the original value for a quicker execution of the job If done the result
26. word size is 5 bits then the 1 s complement of a number a is 11111 a The computer simply inverts all bits of the original number i e executes the logical function NOT Through this segmentation of the initial value range arbitrary but specific all negative numbers have their highmost bit set which plays the role of the minus sign In the q s complement mode the number of positive and negative numbers represented are the same i e even zero has two possible representations 0 and 0 which in binary would be 00000 and 11111 always assuming a word size of 5 bits The 2 s Complement of a number is calculated by adding one to its 1 s Complement Using the same example of word size 5 bits the 2 s Complement of a number a would be 11111 a 1 The 2 s complement of bin 10001 is the number bin 01111 Notice son also in this segmentation the leftmost bit is set for all negative numbers and therefore takes over the role of the minus sign In the 2 s complement mode there is one more negative number than in the positive number range since zero only has the representation 0 The Unsigned Mode no complement Since the Complement mode employs one bit as the negative sign the range of values for a word size of 8 bits in the 1 s complement is from 127 d to 127 d and in the 2 s complement from 128 d to 127 d Note that in both cases those are 256 values For cases when only the positive number
27. 0 c Martin McClure Page 44 of 63 September 2015 HP16C Emulator Module for the HP 41CX 4 2 6 Quick Dec lt gt Hex conversions These two functions perform a quick amp dirty conversion between decimal and unsigned hex values using the real X register and ALPHA Use then when you want to check results independently from the selected base on the emulator The maximum number allowed is H 2540BE3FF or d 9 999 999 999 in decimal Both functions are mutually reversed and H gt D does real stack lift as well These functions were written by William Graham and published in PPC V12N6 p19 enhancing in turn the initial versions first published by Derek Amos in PPCCJ V12N1 p3 4 2 7 Recalling the current base value BASE e The function BASE recalls the value of the current base to the 16X register as an easy way to find it out in a running program The value is pushed into the 16C stack Possible return values in decimal are 2 8 10 and 16 always shown as 10 in their digital display This function is similar to L6WSZ in that both return configuration data to 16X and that in manual mode an information message will also be displayed 4 2 8 Alpha Reverse and Left append character e The function X AL appends the character which ASCII code is in X to the left side of the ALPHA string It is therefore the symmetrical of XTOA This function was written by Hakan Thdrngren and first publishe
28. 000 to the next place occurs at 16 d The table below shows the correspondence between binary decimal and hexadecimal numbers up to 15 d As you can see on the table Hex numbers are the natural choice to represent four binary digits 4 bits therefore the hexadecimal 6 0110 6 number system uses the 4 bits of a nibble in the full value range Each nibble can represent values from bin 0000 to 1111 of in hex from 0 to g 1000 8 F This number system is often used in computer science g 1001 9 B 1012 1 Representation of negative Numbers D 1101 13 When using a limited count of digits m to represent numbers the 1110 value range to the numbers to be represented n is 0 lt n lt 24m 1111 meaning that the greatest number will be 2 m 1 Note that no negative numbers are included in this system of notation To remove this deficiency the concept of complement is introduced The Complement from a reference K The K complement of a number x is defined as the difference from K of that number Com x K x for which k is fixed by the chosen complement Since in the binary number system the usual values of K are 2 m and 2 m 1 we usually speak of one s complement or the two s complement representing the difference from either the greatest number represented or the one after it In general for any base system b there will be a b and a b 1 comple
29. 6Y level of the 16C stack In any case the final result will only be shown in manual mode not if the function is executed in a program The program below illustrates the method used for the adjustment of the result calculated by the 16SQRT function The actual implementation is more clever and splits the execution between an intial MCODE part and a final FOCAL adjustment only done when needed 1 LBL 64SQRT 2 CF 05 3 CF 06 4 32SQRT 32 bit square root 5 LOW16 replicate result in 16C stack 6 LST16X recall input x 7 16RDN place it in 16T level 8 16 calculates sqrt x 2 9 16RUP recall x to 16X 10 16X Y is x sqr x 2 11 SF 05 yes set flag 5 12 16X gt Y is x gt sqr x 42 13 SF 06 yes set flag 6 14 LST16X recall sqrt x to 16X 15 FC 05 were they different 16 GTO 05 no the result was ok 17 FS 06 was it greater GTO 06 no skip adjustment yes subtract one always lt 2432 sets carry show result done The square power 16X 2 is a subfunction available for keytroke convenience as it is assigned to the X 2 key on the 16C keyboard It uses the main 16 code with 16Y equal to 16X thus it is completely equivient to the sequence L16ENT 16 There is no byte savings in a program using either of those approaches 4 bytes will be used Therefore you need to keep in mind that two levels of the 16C stack will be used Note that following the standard conventions the input parameter is left in the LST16X
30. 8 FS 03 9 16 9 SFO5 Apart from that the programs are 10 MASKR 10 16 practically identical to the original ones 11 AND 11 FS 05 on the real 16C machine 12 HEXM 12 SF03 13 SHOW 13 SHOW 14 RTN 14 RTN Examples Extract bits 2 5 from the value H 39 or b 111001 Keystrokes Result Comment HEXM H XXXX current 16X contents 16NPT 3 9 R S H 39 enters 39 in 16X 2 H 2 lifts 16C stack 7 H 5 lists 16C stack XEQ bXT H E or b 1110 c Martin McClure Page 28 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 2 New functions not present on the original 16C This section needs to start describing the other function launchers one of the more relevant additions to the functionality of the emulator not available in the real 16C machine There are two kinds of launchers those that group functions by complementary operation like 2ROT and XSHF and those that do it according to a functional criteria such as 2MOD XBIT XLEFT and XRGHT Note the consistent use of the sigma letter in their names to denote a launcher funtion 3 2 1 Rotations Launcher XROT This launcher groups the 8 rotation functions into two screens one for operation excluding the Carry bit and another for the operation including it Once it is up on the display you will use the key to toggle between each screen as shown below Where the only visible clues are the SHIFT annunciator and the C added to the screen
31. Binary Base display none changes displayed base 17 Cb__ Clears bit value in 16X bit in prompt result in 16X argument to 16L 18 DBL Double precision 16 values in 16X and 16Y Result in 16X amp 16Y stack drops 19 DBL Double Precision 16 values in 16X 16Y 16Z pushes value into 16C stack 20 DBLR Double Prec Remainder values in 16X 16Y 16Z pushes value into 16C stack 21 DECM Decimal base display none changes displayed base 22 FLOAT Floating Point mode none supresses displaying mode 23 HEXM Hexadecimal Base display none changes displayed base 24 LY Left Justify value in 16X Result in 16X pos in 16Y 25 MASKL _ _ Builds a Left justified Mask of bits in prompt pushes value into 16C stack 26 MASKR _ _ Builds a Right justified Mask of bits in prompt pushes value into 16C stack 27 NOT Logical Inversion value in 16X result in 16X argument to 16L 28 OCTM Octal Base display none changes displayed base 29 OR Logical Addition values in 16X and 16Y Result in 16X stack drops 30 RL Rotate Left one pos value in 16X result in 16X argument to 16L 31 RLC Rotate Left thru Carry value in 16X result in 16X argument to 16L 32 RLCN_ RLC n positions value in 16X and prompt result in 16X argument to 16L 33 RLN_ Rotate Left n positions value in 16X and prompt result in 16X argument to 16L 34 RMD Division Remainder values in 16X and 16Y pushes value into 16C stack 35 RR Rotate Right one pos value in 16X result in 16X argument to 16L 36 RRC Rotat
32. C TESTING 16APN 16NPT _ 16RCL_ 16570 br LDZER LOW16 MASKL __ MASKR __ leWwWSZ __ mms oi amp o he New Functions EBIT _ LEFT _ EMOD _ RIGHT _ EROT _ 16C _ 16KEYS _ 16W57 16Kann 16X 2 16X lt gt _ 16X gt 0 16X gt Y 2DIV 2MLT A2FX BASE CHKBB CL165T CLRFX D gt H DGDE DGU DGRV EX2FX FCAT _ FX EX FXSZ GET16 H L H gt D L lt gt H L H MNV NAND NOR REV RJY SAVE16 SIN _ SRN _ TS L WSFIT WSMAX xK 0 KFY M LA ic c Martin McClure Page 63 of 63 September 2015
33. CX Function Carry Out of Range 16 16 yes yes Result gt max ws 16 no yes Result gt max ws gt OOR 16 yes yes RMD 0 gt CY 16SQRT yes no RMD 0 gt CY 16X 2 no yes Uses 16Y and 16X regs 16CHS 16ABS no yes very CMP dependent DBL no cleared y x gt X amp Y DBL yes cleared y amp z x gt X RMD 0 gt CY SL N SR N ASR yes no may push msb Isb gt CY RL N RR N yes no may push msb Isb gt CY RLC N RRC N yes no may push msb Isb gt CY 16X lt gt Y 16X lt gt no yes 16X gt max ws gt OOR 16RCL LST16X no yes 16X gt max ws gt OOR 16RDN 16RUP no yes 16X gt max ws gt OOR CL16X CL16ST no cleared 16WSZ no yes 16X gt max ws gt OOR Table 3 1 Functions affecting the status of CY and OOR flags e Blue font functions denotes additional OOR conditions beyond the original 16C machine e SLN and SRN are new additions in the emulator They behave like the rotation counterparts and only set clear CY on the last position shifting e max ws is the maximum value that can be represented within the selected ws max ms 2 ws 1 See appendix Al for a complete table and sub function WSMAX for their calculated values No Leading Zeros flag LDZER Since flag 3 is reserved for Carry that means the Leading Zeros functionality from the 16C is not available on the emulator in the same way zeros are always omitted by default as it was described in the data inpu
34. HP16C Emulator Module for the HP 41CX HP IBL EMUL HP H Module EN aati 5 mm Ti z ATTA CLLAS Tl Stic eo a REG PREFIX WINDOW esp Bl e JZ oe My z MILGA o h a o WSIZE MOAT 4 HP 60 2 USER 0 34 PRGM ALPHA Written and Programmed by Greg J McClure and Angel M Martin September 4 2015 c Martin McClure Page 1 of 63 September 2015 HP16C Emulator Module for the HP 41CX This compilation revision 1 5 3 Copyright 2015 Angel M Martin and Greg J McClure Published under the GNU software licence agreement Original authors retain all copyrights and should be mentioned in writing by any part utilizing this material No commercial usage of any kind is allowed Screen captures taken from V41 Windows based emulator developed by Warren Furlow See www hp41 org Acknowledgments Special thanks go to Greg McClure for his tremendous work on the 16C Emulator module his 16C Buffer design and handling routines together with the big math algorithms are the heart and soul of this module Thanks to Monte Dalrymple for his feedback on the overlay and this manual and for his thorough testing of the beta software and release candidates Thanks to Michael Fehlhammer for making the 16C overlay a reality in such a short time even before the module release c Martin McClure Page 2 of 63 September 2015 HP16C Emulator Module fo
35. O and the LSB at the rightmost position of W3 Therefore the binary bit stream is as follows B 1001 001 100 101 100 000 001 001 101 101 Summary of Data formats used throughout the registers Data is stored in different formats depending on the registers they are in The lower bits registers in the standard stack are stored in BCD Binary Coded Decimal format thus you can see them like regular decimal values if you exit the displayed prompt from the 16NPT output say for instance pressing the back arrow The higher bits registers in the 16C buffer are stored in binary format i e Non normalized numbers or NNN s Realize that for any math operation the lower bits first will be converted to binary and only then the operation will be applied The visual representation in the Window buffer registers is stored as character digits in ASCII code It may take up to 64 characters therefore there are 8 Window registers like in the original 16C machine Realize that whilst the ALPHA register is the repository for SHOW the information shown in the WINDOW screens uses the LCD as a vehicle instead 16T 16Z 167 16X EX Binary NNN FX ASCII ALPHA c Martin McClure Page 18 of 63 September 2015 HP16C Emulator Module for the HP 41CX d WHAT S NEW A IIFFERENT 3 1 Differences from the original 16C The obvious differences are the dedicated hardware like the keyboard layout and the LCD These account
36. Right n positions o RL _Rotateleft RR_____ Rotate Right RLN Rotate Left n positions RRN Rotate Right n positions RLC Rotate Leftthru CY RRC Rotate Right thruCY RLC RLC n positions RRC RRC n positions STATUS Shows the Status STATUS Shows the Status Use the H character for the hash pound symbol XLEFT is a main function but XRGHT is located in the Auxiliary FAT with index 2 Note also that the main four launchers are interconnected and can be navigated sequentially using the XEQ key Refer to the chart in next page for a complete representation of the options Launchers as sub functions There are four launcher functions located in the auxiliary FAT thus implemented as sub functions in the 16C Emulator module SSHF XBIT XRGHT and X 0 Because sub functions are always programmable i e cannot be declared as non programmable when you execute them in program mode the function itself will be entered into the program This means you cannot use them this way in program mode to directly access their menu choices as it happens in manual mode To work around this limitation you can use their parallel launchers which as main functions are properly declared as non programmable and toggle their functionallity using either the SHIFT key and or the anchor key A as follows for X 0 options for ERGHT options for XSHF options for XBIT options Naturally yo
37. ag annunciators are temporarily borrowed by 16NPT to show you which partial you re working on at any time Thus you ll see 1 12 or 123 depending on which one of the three partial screens you re in at any given time Once completed their status will revert back to their previous values prior to executing 16NPT Note that the back arrow key will either delete the current digit or cancel the function if there are no more digits left on the display This will show the value in 16X previous to the execution of 16NPT or enter the current partials already committed to if a partial entry had already happened Note as well that only 12 characters are displayed on the LCD at a given time If you enter more the previous will be scrolled to the left and removed from view but not lost not to worry about that The back arrow removes the rightmost digit but won t scroll the string back to the right The digit entry is terminated pressing or indistinctly upon which the information is shown as alphanumeric string in ALPHA scrolling if larger than 12 and transferred to the 16CX register The 16C Stack is lifted as you d come to expect same as with the standard stack At that point you re done and ready to move on to the next action There are several usability features built into the 16NPT function that make it easy to use and as closer to the original 16C as reasonably possible balancing the code requirements and the general
38. al _ a a n l Tn fi tp En 9 Tn The program uses the initial estimation x0 6 log S Data registers RO1 and R02 are used to store the successive approximations Xn 1 LBL 645QRT 2 CF 21 3 16X MA 4 LOG 5 E 6 7 LOW 16 8 165TO 9 LBL 00 10 16RUP 11 16X A 12 16RCL 13 16 14 LST16X 15 16 1 amp 6 2 17 LOW16 18 16 19 16ENT 20 16X lt gt 21 16X lt gt 22 16X Y 23 GTO 00 24 SHOW 25 END Example Calculate the square root of ABC DEF ABC DEF 16NPT ABCDEFABCDEF gt H ABCDEFABCDEF XEQ 64SQRT gt H D1B7FD c Martin McClure Page 51 of 63 September 2015 HP16C Emulator Module for the HP 41CX Appendix B3 Showing leading zeros A FOCAL reprise The program below is a parallel version of the MCODE function available in the module it basically uses the same method so you can see how it s been implemented in particular is a good example of the BASE function 1 LBL LEAD 2 165TO 00 3 WSZE 4 STO 00 5 0 6 KF 7 BASE g LN 9 2 10 LN 11 J 12 FIX amp 13 RND 14 SFINDX 15 FRC 16 a0 17 GTOOS 18 RCLOO 19 LASTX 20 n ENTER 22 INT 23 W 24 ISGY 25 NOP 26 RDN 7 3 28 AROT Ssave value get word size put in ROO reset flags i2 B 10 16 bits char rounded flag case remainder was it decimal yes do nothing ws bits char chars make integer was it round no add one chars r
39. ample pressing 1234 ENTER pushes the real number 1 234 into the Y register but it does nothing good to the 16C stack at all just the opposite For a proper 16C value entry you must use 16NPT at all times even in its quick entry and shortcut modes Thus the right keystroke sequence will be LENPT 1234 ENTER Not much more elaborate as it only requires the 16NPT as a prefix This function will lift the 16C stack automatically so no need for a final 16ENT at the end in this example Similarly other stack manipulation and memory exchanges need to use the 16C versions instead of the native standard ones Here is where the Ife keyboard comes to the rescue as it has most of them pre assigned to their logical positions like 16STO in the key L6RDN in the key etc All you need to remember is a ways press the 16C launcher key first then the 16C function to complete the action Using the F launcher is a more convenient method than populating the 41 keyboard with multiple standard key assignments for three reasons It doesnt prevent the standard functions from being available in USER mode It allows direct access to both main functions and sub functions equally It doesnt take extra memory registers to hold all those many key assignments However if those points are not an issue you can always re configure the entire 41C keyboard using ASN to map the main functions won t work for sub functions as you find it mor
40. an extended memory file Note that even if you can have multiple X Mem files with different 16C stack sets obviously with different file names there can only be one on line at any time When you execute GET16 there s a check prompting for confirmation Realize that this action will override the existing 16C buffer replacing it with the data from the X Mem file Only the Y N keys are active at this prompt Upon termination the function will show the current value in the 16X registers in RUN manual mode either the current one for SAVE16 or the newly retrieved one in the GET16 case Also the mode annunciators 0 1 2 will be changed appropriately if different If you re using the OS X extension module you ll notice that these files will be identified with the character H during the CAT_4 enumeration Also note that 16C stack files are always 25 registers long 20 for the buffer plus 5 for the X Y Z T L stack 1 2 3 4 Notice how the X Mem file really occupies 28 5 register in X Mem as there are three E additional registers needed by the OS to 7 manage it within the X Mem file system g The file header register is the second one 7 starting from the bottom This address can 11 be retrieved using the function FLHD 2 available in RAMPAGE module amongst 13 others 14 15 The buffer address can be obtained using 16 function BUFHD available in the RAMPAGE 17 module as well with several others for 18 buff
41. as all buffers are refreshed by the individual modules that require their use The 14 is the buffer size in hex requires 20 registers The f is the Silent Loud mode flag used for message displaying Nothing more is stored in this header Note that the S amp X field is used by function BFCAT and therefore is reserved Buffer registers 00 and 01 The 00 and 01 register hold a calculated mask that will help in making decisions carry status out of bounds conditions etc on the status of arithmetic and logic functions It is related to the word size bb and is described below For word size lt 32 All 01 m fields will be 0 i e it will contain 01 000000000 Ocd The 00 m fields will represent the bits allowed in values to be saved and used Some examples are 00 OFFFFFFFF 020 for 32 bits 00 OOOOOFFFF 010 for 16 bits etc For word size gt 32 All 00 m fields will be F i e it will contain 00 OFFFFFFFF Obb The 01 m fields will represent the upper bits allowed in values to be saved and used Some examples are 01 OFFFFFFFF Ocd for 64 bits where bb would be 40 01 OOOOOFFFF Ocd for 48 bits where bb would be 30 c Martin McClure Page 53 of 63 September 2015 HP16C Emulator Module for the HP 41CX The cd bits in buffer register 01 show the current complements mode c and binary mode d If c 0 no complement mode is set c 1 means 1 s complement is set c 2 means 2 s complement is set These settings influence
42. bility is limited to single digit integers it doesn t get any easier Some typical uses for this functionality include quick arithmetic double half triple etc and integer values used as parameters for other functions The picture below shows the 16C Keyboard Overlay in all its glory where the options for LENPT LOW16 and the digit pad are shown in red color gt BIT S 16SQR 16x lt gt 16RUP LFT R MASKL MASKR FCAT 16ABS x 0 HP 16C Emulator All functions shown on this overlay require pressing the fe main launcher first Note You can assign the 16C function to any location on the keyboard Because it is used very frequently it s recommended you change that location from time to time to avoid the associated hardware wear amp tear on the key domes Always ensure that Revision O1 or higher of the Library 4 is installed on the system c Martin McClure Page 16 of 63 September 2015 HP16C Emulator Module for the HP 41CX 2 3 Data Output When executed in manual mode RUN every function in the 16C Emulator module terminates the execution by calling the data output routines also directly available in function SHOW This presents the result value as a possibly scrolling string of digits in the ALPHA registers preceded by the base indicator on the left For a more effective presentation SHOW will leave out the padding zero characters to the left of the first significat digit regardless of the selecte
43. both display and calculation flag results If d 0 floating point mode is set and the HP41 registers act as normal no emulation is in effect If d 1 then bin mode is in effect d 2 means oct mode d 3 means dec mode and d 4 means hex mode Buffer registers 10 thru 14 When bin oct dec or oct mode is in effect and word size gt 32 then these buffer registers contain the upper bits beyond the 32 stored in the standard stack For example if the HP 16 X register should contain the hex value 1234 5678 9ABC DEFO then buffer 13 will contain 13 012345678 000 and actual HP41 register X will contain the floating point value corresponding to 9ABCDEFO that is 2 596 069 104 This is done to insure the registers can always been viewed in floating not have weird Non Normalized contents The same pairing of a buffer register and a stack register exists for each of the stack registers thus emulating the HP 16 64 bit binary stack The pairing is as follows Buffer register HP41 stack register HP 16 emulated register Binary T 16T Binary Z Binary L Buffer registers EO thru E3 These buffer registers are scratch registers They are used for holding partial results for holding the dividend when translating binary output to digital representation and for construction of binary values on user input Their purpose changes based on the function being simulated The masks of buffers 00 and 01 are applied here to insure values are
44. d in PPCJ V13 N7 p9 It is used as a subroutine by the Leading Zeros functionality within the function LDZER e The function AREV does a mirror image of the ALPHA register contents It was written by Frans de Vries and first published in DF V10 N8 p8 It is used as an internal subroutine by the Digit Reversal within the function DGRV Copyright Message Easter Egg So you can amuse your friends a copyright message with a fancy sound can be invoked using the c function with index 060 in 16 to access this message c Martin McClure Page 45 of 63 September 2015 HP16C Emulator Module for the HP 41CX APPENTICES a l Maximum values as function of word size 44 a 2 The Hexadecimal Number system 45 b 1 Program Examples 48 c 1 Buffer Technical Details 51 Buffer Registers Explained Input Output Routines Multiplication Routines Division Routines Addition Subtraction Routines LFT R MASKL MASKR STATUS WINDOW HP 16C Emulator Martin McClure HP 16C Emulator 16NPT Hot keys c Martin McClure Page 46 of 63 September 2015 HP16C Emulator Module for the HP 41CX Appendix A1 Maximum Values depending on the Word Size The table below shows the maximum possible values that can be represented as a function of the selected word size These values are also returned by the function WSMAX for the current selection of ws in floating point format native to the 41C OS Ws max value ws max value
45. d word size This includes the 16C stack and memory handling function like 16X lt gt Y or 16RCL so the user can always expect to see a proper integer digital value as result of the operation This presentation will be omitted when the functions are executed in a program with the exception of SHOW itself which will put the result in ALPHA and stop the program if the user flag 21 is set as it is the case for the native function AVIEW Another possible option to visualize the value in the 16X register is the function WINDOW Like in the original 16C it presents the value across a variable number of 8 character windows as many as needed to cover the actual length of the value For instance in binary base with a word size of 56 it may take up to 7 windows to review the complete result maybe less since here too padding zeros on the left won t be shown Contrary to the original 16C however the listing starts with the MSB in window O the first one and this will always be shown when you call the function The succesive characters will be placed in the following windows until the LSB is placed in window 6 for the example mentioned above The user can navigate sequentially through the windows pressing the and keys or randomly get into any specific window by presing its corresponding number from 0 to 7 on the number pad You ll then use the back arrow key to leave the show so to speak The windows are numbered from WO
46. ding Zeros Cb__ Clears bit B Separator shows Sb__ Sets bit DGRV_ Digit Reversal b ___ Isbitse Use the H character for the hash pound symbol One of the main advantages of these launchers is that they provide direct access to both main and sub functions in their choices You should also note that the functions 16 and 16 are also included in the choices even if not shown in the LCD just by pressing the USER and ALPHA keys as well So there you have it perhaps a bit of repetition but you have it both ways so no excuse for not being able to access the functions or subfunctions in a split second anymore c Martin McClure Page 30 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 2 4 Left and Right Launchers and The last two group many shifting and rotation functions together using the geometric position as a criteria as opposed to the specifit bit manipulation action as in the previous cases You can think of these two launchers as the two personalities of the same function and as you surely have guessed already you ll use the SHIFT key to toggle between them at will There are 9 functions on each screen as shown on the function tables below q EFT ERG UY eft Justify RY Right Justify REV ReverseBits ASR Arithmetic Shift Right MASKL Mask Left MASKR__ Mask Right SLN Shift Left n positions SRN Shift
47. e Right thru Carry value in 16X result in 16X argument to 16L 37 RRCN_ _ RRC n positions value in 16X and prompt result in 16X argument to 16L 38 RRN_ _ Rotate Right n positions value in 16X and prompt result in 16X argument to 16L 39 Sb__ Set bit value in 16X bit in prompt result in 16X argument to 16L 40 SHOW Shows value in 16X value in 16X Puts value chars in ALPHA 41 SLN_ Shift Left n positions value in 16X and prompt result in 16X argument to 16L 42 SRN __ Shift Right n positions value in 16X and prompt result in 16X argument to 16L 43 STATUS Shows Status Info base and complement data Shows machine status msg 44 UCMP Sets Unsigned mode none changes mode sets flag 0 45 WINDOW _ Shows the Window registers values in FX buffer regs shows FX registers on LCD 46 XOR Exclusive OR values in 16X and 16Y Result in 16X stack drops 47 LLEFT _ Left Launcher prompts for function executes function 48 MMOD _ Modes Launcher prompts for function executes function 49 LROT _ Rotations Launcher prompts for function executes function c Martin McClure Page 7 of 63 September 2015 HP16C Emulator Module for the HP 41CX 50 16C STACK Shows Copyright amp Sound n a Flashes message amp sounds 51 16ABS Absolute value value in 16X result in 16X argument to 16L 52 16CHS Changes 16X sign value in 16X and compl mode result in 16X argument to 16L 53 16ENT Pushes 16X one level up values in 16C stack 16X in entered to 16Y 54 16NPT Main Data I
48. e appropriate Entering lower bit values with LOW16 As an alternative to L6NPT you can also use sub funtion LOW16 for a quick entry mode of values in the lower bits half register With this method you enter the number directly in the X register instead of the ALPHA registers to hold the characters Obviously this only allows introducing digits 0 9 since the standard X stack register is used Besides that the value entered will be normalized to the base and word size conditions in effect by the function so that the end result will comply with the status of the machine Examples with word size 16 and HEX mode selected 12345 16 LOW16 gt H 3039 1234 LASTF gt H 4D2 But with word size ws 8 and BIN mode selected instead 12345 16 LOW16 gt b 111001 which corresponds to 57 in decimal i e the value has been truncated to 8 bits Note pressing the digit pad in program mode fe plus number key is the best shortcut to enter LOW16 in program mode just make sure the number is already input in the previous program line c Martin McClure Page 20 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 2 Flags as Mode Semaphores Personally I always thought that one of the shortcomings on the original machine is that it offers no visual information for the currently selected signed mode Whether it is unsigned 1 s or 2 s complement there s no indication on
49. e routine first checks to see if it may need a sign change 1 s complement or 2 s complement mode this check changes the order of the result to buffer order E1 E0 E3 E2 from high order to low order 3 The result in buffers E3 and the BCD expansion of E2 low order are placed into buffer 12 and stack register Y respectively since that is where the low order piece is stored for DBL and buffers E1 and the BCD expansion of EO high order are placed into buffer 13 and stack register X respectively 6 The multiplication routine returns via a routine that translates the values in buffers E0 E1 into buffers FO thru F7 and displays the result Some of the seemingly redundant moves of values are explained by the fact that the change sign routine described later works on data in buffers E1 and E0 Routines exist for easy exchange of buffers E1 and EO with E3 and E2 and for taking buffer 13 and the binary of stack X and putting it back into buffers E1 and E0 Taking advantage of these routines dictated these moves Also note that for DBL no stack drop is required at the end since the multiplicand and multiplier are replaced with the double precision result c Martin McClure Page 57 of 63 September 2015 HP16C Emulator Module for the HP 41CX The cross multiplication step is carried out by taking the multiplicand and multiplier and separating them into 16 bit chunks This is required because there is no multiply instruction for the in
50. elected word size thus the higher bits register will be empty when the value can be expressed by 32 or less number of bits The 16C Stack is the first abstraction layer you need to become familiar with Like its standard counterpart X Y Z T L the 16C Stack consists of 5 logical 64 bit registers named 16X 16Y 16Z 16T and 16L or Last16X Physically each one of these is made as the logical combination of the standard stack register of the same name plus another register from the 16C Data Buffer As you d expect the standard stack contains the lower bits half of the value whilst the buffer register holds the higher bits 16X X MZ Z eT T 16L X o o OoOO Y 16Z ZL T oOo L 2 1 1 16C Stack Operation functions A set of functions is provided to operate on the 16C registers as whole unit including both the lower and upper bits halves simultaneously It is important that you remember that the standard functions of the calculator will only access the lower bits halves and thus you should use the 16C functions instead unless you re already on the grand master level and begin hacking around These functions include the 16C stack handling usual suspects here 16ENT 16X lt gt Y 16RDN 16RUP CL16X CL16ST as well as exchange with the other data registers in the calculator memory 16STO 16RCL and 16X lt gt The last three are also programmable using the non merged approach w
51. er management in case you re interested 19 20 71 23 24 25 aLi i 26 bHeader bHeader 27 File Header 28 c Martin McClure Page 38 of 63 September 2015 HP16C Emulator Module for the HP 41CX H TTIHGNGSTILCS 4 0 Silent and Loud Modes TS L Without a doubt the Carry and Out of Range flags area vital component of the information displayed during the execution of the calculations However it s not difficult to miss a particular occurrence of these situations or you may find yourself paying extra attention just to catch possible changes of these flags The 16C Emulator offers a training wheels mode to make those situations easier to remark each time the Carry or Out of Range flags are set a corresponding message is shown briefly in the display Besides the visual message also a short tone sounds to alert the user with a higher pitch for CY anda lower one for OOR Note that contrary to the standard 41 OS these messages will flash in the LCD briefly and then they ll go away to show the result of the function executed We have used the text OVERFLOW for the Out of Range warning as it is easier to read during the brief flashing time and to differentiate it from the floating point error from the native 41 OS We ll refer to this as the OOR event nonetheless following the 16C conventions Activating the LOUD mode The SILENT LOUD modes are user selectable executing the sub function TS L to toggle the act
52. est absolute register is shown below and individual sections will be discussed after F7 O bbbbbbbb G01 Input Output sub buffers the Windows of the F6 bbbbbbbb l HP 16 It is used for input of digits for bin F5 bbbbbbbb 1 oct dec and hex modes by user and for output F4 bbbbbbbb G01 of results of function or view F3 bbbbbbbb l In bin mode b 0 or 1 oct mode lt b lt 7 F2 O bbbbbbbb 1 dec mode lt b lt 9 hex mode any hex digit F1 bbbbbbbb 0 1 These digits are store in reverse of display or input F bbbbbbbb nel b bcd digit l number of digits used n negative E3 Qaaaaaaaa 000 Temporary calculation registers EO and E1 are used E2 Oaaaaaaaa 90 several purposes E2 and E3 are for double precision E1 Qaaaaaaaa 90 functions DBL and DBL EO Oaaaaaaaa 900 14 011111111 000 These are the upper 32 bits for the stack registers 13 xxxxxxxx 000 The HP 41 can only save 32 bits of info in its std 12 Oyyyyyyyy 0 stack these hold the other 32 bits of simulated regs 11 022Zzzzzzz 900 10 etttttttt eee Q1 Ommmmmmmm Ocd Mm represents the mask based on word size Wordsize is OO Ommmmmmmm Obb stored in bb c is complement s mode d is calc mode BB 14f000000 xxx Header with buffer id buffer size and loud mode flag BB buffer register Header Let s start with the BB buffer header It is required to identify the buffer and the HP 16 MCODE Emulation module will refresh this header on power on
53. f choice There is therefore no need to exceute any function for visualization just change to the base of choice using one of the four base mode functions BINM OCTM DECM and HEXM These are located in the top row on the 16C keyboard assigned to the B C D and E respectivelly Note Another way to change the base mode is using the SMOD launcher which will be described later in this section The display always shows the base digit on the left so you can tell which based it is expressed on Note that the values in the 16C stach will not change when you modify the base mode they are in binary and BCD as explained before and the value display routine will represent them in the appropriate base as per the current selection These three numbers are indeed very different from each other the base identifier gives them away Don t forget to change the default mode to a digital base no display will occur in FLOAT mode c Martin McClure Page 19 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 1 Number Entry on the 16C Stack By default the 41 keyboard knows nothing about the 16C module The standard functions are always available for real number operation call it the FLOAT mode if you wish This is important to remember as it imposes some discipline on the user to differentiate them from the 16C version of the same functions for instance for number entry and stack handling For ex
54. from right to left starting at position 3 of each register until finished All other Fx buffer registers will contain O length and 0 bcd values The negative indicator would be 0 since octal values do not include a sign After input is completed the bcd to bin translation routine would then create the binary representation of this octal number and place these into the following Ex buffer registers E1 000000002 9800 EO O9C29CDAE 9800 representing binary 2 9C29 CDAE in hex The X register would receive decimal value of 9C29CDAE hex and buffer register 13 would receive the 2 assuming word size gt 34 The output routine will take a value placed in the EX buffer registers and translate them to digits in the Fx buffer registers Then control will be given to the display routines which will use these registers as HP 16 Windows For example assume the binary value in E0O E1 buffer registers are E1 000000222 000 EO 033334444 000 The bin to bcd translation routine would then take these values and translate them to the Fx buffer registers based on mode bin oct dec hex It will first clear all Fx buffer registers then for oct mode the following will be placed into the Fx buffer registers specified F1 000360124 006 F 040121341 nes which represents 42 1063 1431 2104 octal Window 1 on HP 16 would hold 421063 and Window 0 would hold 14312104 Notice these values are read from right to left Again since this is octal n is 0 to re
55. g preventing them to be placed before a normal program line The non merged functions take care of updating the program counter to always ignore the index line so the YES NO do if true rule is perfectly applicable in this case Examples a Correct utilization b Incorrect utilization 01 16 01 FS 25 02 6 02 16 03 GTO 01 03 6 04 GTO 02 03 GTO 01 04 GTO 02 That s the reason why the tests have all six cases including gt which wouldn t be possible to do using a chained double conditional like it is done for the standard OS functions The table below shows the sub function indexes in decimal used for the test conditionals a V 7B gt 8 14 Test Criteria c Martin McClure Page 25 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 6 ISZ DSZ and Function Parameters The HP 41 has its own implementation of the index controlled functions ISG and DSE more flexible than those in the HP 16C and HP 15C which use the HP 67 model with ISZ and DSZ instead whereby a unique indirect register is used and the index value is always made with zero For convenience the emulator includes DSZ and ISZ which use the ROO register to hold the indirect variable I Therefore you won t need to worry about converting the format for 16C program compatibility using ISG and DSE Notice however that this implementation still uses a standard register ROO and not a 64 bit logical register li
56. hereby the target register number is entered as a follow up line in the program c Martin McClure Page 11 of 63 September 2015 HP16C Emulator Module for the HP 41CX 2 1 2 Stack and Memory Functions The table below summarizes all functions and sub functions related to stack and memory handling Lifts 16C Stack Lifts 16C stack Lifts 16C stack Uses two data regs Lifts 16C Stack Uses two data regs Creates H type file Note that 16STO 16RCL and 16X lt gt are prompting functions As explained before two data registers are used to store the 16X values in memory Refer to the table on the left for a correspondence between the register used in the prompt and the actual SIZE required in the calculator to allow for the range of 16C data registers needed Note that ROO is used by the ISZ and DSZ sub functions as the indirect register therefore and to avoid conflicts the actual registers usage in the 16C registers scheme begins with RO1 amp RO2 for the 16C version of 16R00 This makes them compatible with each other so you don t have to worry about it Remember that you can also use the 41 native functions ISG and DSE instead for a more powerful implementation that allows you to choose the indirect register used In that case you need to mind the potential register conflicts Now that we ve got the data requirements and design considerations out of the way let s see how to go about introduc
57. id on the left The function table is below RL Rotate Left RLC Rotate Left thru CY RLN___ Rotate Left n positions RLCN__ RLCn positions RRN__ Rotate Right n positions RRCN___ RRCn positions o RR_ k Rotate Right RRC Rotate Right thru CY 3 2 2 Shiftings Launcher XSHF This launcher groups 4 bit shifting functions in the first screen plus another 4 bit manipulation functions in the second Once it is up on the display you will use the SHIFT key to toggle between each screen as shown below SL Shift Left DGU Digit Left Justify ILN__ Shift Left n positions LIY Left Justify RN__ Shift Right n positions RJY Right Justify SR _ Shift Right ASR Arithmetic Shift Right Remarks Both the Rotations and the Shifting launchers expect you to choose the option using the top row keys B to E as per the screen layout Hitting the anchor key A in the non shifted screen will move back and forth between these two launchers the Rotation and the Shifting screens Pressing the back arrow keys cancels the function and displays the current value in the 16C register again c Martin McClure Page 29 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 2 3 System Modes Launchers and Moving on now to the functional criteria launchers they have in common that the prompt includes the different choices as a s
58. ier saving the state of the combined signs in one of the CPU internal registers G in case you re curious 3 The high order of the absolute values of the multiplicand and multiplier are saved back to buffers 13 and 12 the low order bits are saved to buffers FO and F1 respectively Thus multiplicand is now in buffers 13 FO multiplier is now in buffers 12 F1 4 Now a full cross multiply is performed using 16 bits at a time thus 16 total cross multiplications into buffers EO low order thru E3 high order this is the core part of the multiplication routine This routine is explained later in this section 5 Notwithstanding a lot of weird code that checks for overflow or carry flag conditions the routine then divides into single precision 16 and double precision DBL result sections Here are the two possible paths a For SINGLE PRECISION the result may need a sign change 1 s complement or 2 s complement mode then an extended stack drop is performed including buffers 10 thru 12 dropping down to buffers 11 thru 13 and the contents of the result in buffers E1 and the BCD expansion of EO are placed into buffer 13 and stack register X respectively b For DOUBLE PRECISION three steps are required 1 The result needs to be shifted so that the proper bits are separated into E3 E2 for high order and E1 E0 for low order based on word size both buffer register pairs need to contain values within the word size required 2 Th
59. ignore the input for parameters larger than the maximum word size 64 A warning message reminding of the current word size WS nn will be shown if the parameter entered is larger In a running program the message shown will be OUT OF RANGE in those instances and the execution will halt at the current program line Entering 00 will toggle between complementary function pairs i e change MASKL into MASKR RRN into RRCN RLN into RLCN SLN into SRN and vice versa This does not impact the bit selection functions Cb Sb and b for which zero is a valid input value Pressing SHIFT will activate the INDirect facility i e the parameter is retrieved from the standard data register entered at the prompt No support for STack registers is provided so do not use IND ST_ even if you can bring that option to the display When you enter the functions in a program the prompt will be discarded by the OS so you can fill it with any values In a running program the parameters are taken from the 16X register the same as in the original machine Just fill the prompt with any values when you enter the function they ll be ignored by the OS at that point Note that in program mode a zero or values larger than the current word size will also trigger an out of range condition c Martin McClure Page 24 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 1 5 Test Functions Launchers You
60. in 16Y 27 SAVE16 Saves 16C buffer in X Mem X mem file name in ALPHA buffer saved in X Mem file 28 SL Original Shift Left function value in 16X result in 16X argument to 16L 29 SR Original Shift Right function value in 16X result in 16X argument to 16L 30 WSFIT Fits the word size to 16X value value in 16X ws changed 31 X 0 _ Tests to zero Launcher XO tests launcher executes function 32 XNOR Negative XOR values in 16X and 16Y Result in 16X stack drops 33 BITS Gets sum of selected bits value in 16X Returns sum of bits to 16X 34 FCAT _ Sub function Catalog has hot keys enumerates sub functions 35 TESTING Section header section header n a 36 16KEYS Mass Key Assignments Prompts Y N Makes Removes KA 37 16WSZ Retrieves current word size set ws data from buffer Shows ws and puts it in 16X 38 2DIV Halves the content of 16X value in 16X result in 16X argument to 16L c Martin McClure Page 8 of 63 September 2015 HP16C Emulator Module for the HP 41CX 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2MLT A2FX BASE CHKBB CLRFX D gt H DGD DGLJ DGRV EX2FX FX2EX FXSZ H gt D H L L H L lt gt H LDZER MNV TS L WSMAX X LA c Doubles the content of 16X Alpha to FX registers Recalls base to 16X Checks amp Builds the 16C buffer Clears FX buffer registers Decimal to Hex Decimal Digit Sum Digit Left justify Digit Reversal Copies the EX regs to the FX regs Copies the
61. in FAT or even functions located in other plug in modules if the function name is not found in the auxiliary FAT the search continues automatically through all the modules plugged on the 41 system and only if no match is found the NONEXISTENT error message is displayed Obviously there s a noticeable time penalty associated with all this but one that it s totally unpercieved on the 41 CL set in TURBO 10 or higher in case you wonder LASTF Operating Instructions The Last Function feature is triggered by pressing the radix key decimal point the same key used by LastX while the launcher prompt is up This is consistently implemented across all launchers supporting the functionality in all four modules they all work the same way When this feature is invoked it first shows LASTF briefly in the display quickly followed by the last function name Keeping the key depressed for a while shows NULL and cancels the action In RUN mode the function is executed and in PRGM mode it s added as two program steps if programmable or directly executed if not programmable If no last function yet exists the error message NO LASTF is shown If the buffer 9 is not present the error message is NO BUF instead The LastF buffer is maintained automatically by the modules created if not present when the calculator is switched ON and its contents are preserved while it is turned off during deep sleep No
62. in range and to determine the proper carry and out of range flag settings An example of their use for digit input and display output is show in the discussion of the FO thru F7 buffer registers 7hey cant be counted on to hold any values of use between functions and can be overwritten by any function needing them Buffer registers FO thru F7 These buffer registers hold the digit representations of the binary values input from the keyboard or the digit representations of the binary values to output to the display Similar to the Q register on entry of some kinds of alpha data binary values are written in or read out in reverse order For the multiplication and division routines some of these buffer registers are also used as scratch registers The input routine takes digits entered by the user and stuffs them into these registers from right to left starting at FO and continuing to F7 The number of digits entered in a particular register is placed as the rightmost digit of the buffer and up to eight digits can be entered into positions 3 thru 10 of each register This allows up to 64 digits max possible for binary value with max word size to be entered As an example in oct mode 1234 1234 5656 is entered by keyboard The contents of buffer registers FO and F1 will contain F1 000006565 004 F 043214321 hn 8 c Martin McClure Page 54 of 63 September 2015 HP16C Emulator Module for the HP 41CX Notice that the digits are entered
63. ing and reviewing actual 16C values in the calculator c Martin McClure Page 12 of 63 September 2015 HP16C Emulator Module for the HP 41CX 2 2 Data Input 16APN If the 16C buffer is the invisible heart of the module then the 16NPT function is its visible counterpart This is the function youll be using most of the time to enter the data values and arguments for your calculations regardless of the selected base and complement mode set When invoked the function prompts for the digit values to input showing the selected base on the left side of the display The data is input as alphanumerical digits on the LCD display during the process Only the appropriate digits for each base will be allowed You can enter up to 24 digits at a single time or split the entry in three different sub sections called partials if so preferred Obviously for large values in Binary mode this last method will become necessary but for all other bases a single partial is enough to hold the maximum numbers allowed even for a 64 bit word size The digit entry can be completed only partially by pressing the key this will commit the digits to the 16C buffer and will present the base prompt anew ready for the next partial entry The second partial is then appended to the first one and this can be repeated again for the third and last partial so even a 64 bit value in binary can be entered using three segments of data The fl
64. ises and extensions added to the design Support for up to 64 bit word size is provided in all functions beyond any previous attempt implemented on the 41 system ever before The design takes full advantage of the alphanumeric capabilities of the 41 in particular the 24 character LCD for more convenient number entry and display Prompting functions and X Memory backup enhance the usability and go beyond the original machine Use them in manual operation or in a program all functions are completely programmable Auxiliary FAT Bank switching and Page 4 Library The 16C Emulator module comes loaded with functions and a rich feature set yet it only takes a single page i e half port on the 41 ROM module bus Its structure consists of four bank switched 4k blocks with functions arranged in two Function Address tables the main one filled up with 64 functions plus an auxiliary one containing additional sub functions All are programmable and easily accessed using dedicated function launchers Plus a complete 16C Keyboard overlay is available for instant plug and play functionality it makes extensive usage of the library routines for more efficient execution as well as management of the auxiliary FAT and sub function launchers which relies on the presence of the Library 4 installed on the system The Library 4 has been updated for the 16C Emulator thus The last remark is regarding the CX dependency designed for the CX version of
65. ive mode Of course you can also use the numeric launcher 16 with index 054 When you do the mode selected is also briefly shown in the display plus a dual tone if you re toggling to LOUD mode The CY OOR messages air time will be variable as it depends on the subsequent operations performed during the execution of the function For 41CL users the implementation is compatible with the current turbo setting so you won t be missing them even if the CPU is running at high speeds Independently form whether you are a casual user or a seasoned digital design engineer you may find this functionality useful neutral or plain hideous in which case all you need to do is ignore this section altogether as the factory default setting is SILENT mode Go ahead and try it out to get the feeling and decide for yourself It comes without saying that the flags annunciators will continue to be displayed as well in Loud mode Lastly and as you can expect the messages will not be displayed when the functions are executed in a runnng program c Martin McClure Page 39 of 63 September 2015 HP16C Emulator Module for the HP 41CX 4 1 An alternative to the 16C keyboard 16KEYS If you prefer a more direct approach to access the 16C Emulator functions in an automated way the sub function L6KEYS will prepare a standard key assignment based complete keyboard re definition for all those main funcions from the 16C keyboard to be as
66. ke it is the case for the 16C stack or the other registers as accessed by 16STO and 16RCL While it is safe to assume that loop counters and other parameters won t exceed the 32 bit limit you can always convert the index into a 64 bit format using LOW16 in case that is required Similarly the parameter for LGWSZE can only go up to 64 so it s a bit of an overkill to allocate 64 bits for that one too therefore you can just use a standard value in X and 16WSZ will accept it as a valid input Remember however not to disturb the 16C stack by doing so Contrary to this situation the masking bit shifting and rotation functions expect 16C formatted values when used in a program for the number of positions or number of bits in the MASKL R case thus you shouldn t use the standard X reg workaround with them As a reminder the three proper ways to do it are a String value in ALPHA plus L6NPT and optionally 16APN or a decimal value in real stack X register plus LOW16 or avalue from 16RCL 16X lt gt or any other 16C stack operation Registers and Word Size changes There is no effect of a word size change in the data stored in the data registers This is different from the real 16C machine which adjusts the values in memory to fit the currently selected word size spilling over adjacent registers in case of a wordsize decrease and splitting across registers in case of a wordsize increase Put in another words the
67. lated functions 35 3 4 3 Left and Right Justification 36 3 4 4 Bit Reversal 36 3 4 5 Multi Position Shifting 37 3 4 6 Storage and Retrieval in X Memory 38 4 Diagnostics Functions 4 0 Silent and Loud Modes 39 4 1 An alternative to the 16C keyboard 40 4 2 A few Development Aids 41 4 2 1 Buffer Registers handling 41 4 2 2 Buffer Data Types 42 4 2 3 Doubling and Halving 42 4 2 4 Digit Justification Reversal and Decimal Sum 43 4 2 5 Test for Maximum Negative Value 44 4 2 7 Recalling the current Base value 45 4 2 8 Quick Hex lt gt Dec 45 a l Maximum values as function of word size 46 a 2 The Hexadecimal Number system 47 a 3 Program Examples 50 a 4 Buffer Technical Details 52 Rin RAN MASKI Rl RR w p E f ri i ALC aT RALEN ARC oe ans a a za Ea cia ee E a ee ee P CLEAR r Bt COML PRGM REG PREFIX VANDOW r s zs p 4 faso 2 2 He PSE TA WSIZE FLOAT STATUS lt 3 _ ry eh T ks oN I lt i j Ea Es HEWLETT PACKARD c Martin McClure Page 4 of 63 September 2015 HP16C Emulator Module for the HP 41CX HFP IBE Emul ator Modul Computer Science for the HP 41CX 1 Introduction At long last a complete solution for the Computer Scientist on the HP 41 platform is finally available in the form of the HP 16C Emulator module This module provides a comprehensive feature set that includes all the functionality from the original HP 16C plus a few new surpr
68. ment like the 9 s and 10 s complement in the decimal system where b 10 Distribution of ranges of values If there seems no reason yet for the existence of complement notation remember that to this point we haven t dealt with negative numbers We shall include these by adopting an arbitrary distribution of value ranges in our number systems For instance in the binary system we l define a negative number as one which most significant leftmost bit is set has a value of 1 Arranging number distributions and using complements change the ranges of values as follows No Complement 0 lt x lt b m 1 b Complement b m 1 lt x lt b m 1 1 b 1 Complement b m 1 1 lt x lt b m 1 1 Basically in the signed modes with complement we divide the original total value range b m 1 in two half sections allocating one of them for negative numbers and the left over for positive c Martin McClure Page 48 of 63 September 2015 HP16C Emulator Module for the HP 41CX Complement Signed Modes The transformation of decimal numbers represented in the binary system and vice versa varies with the signed mode used The three modes are Unsigned mode no complement only positive numbers 1 s complement mode 2 s complement mode The 1 s Complement of a number is calculated by subtracting this number from the greatest representable number in the chosen word size number of bits For instance say the
69. no skip line Z 2 Z OOOO RLRR C C 1 S amp X locationofbE1 ss RLRR PLA 96 C C A S amp X pointer to bEO bE1 RLRR 28C FSET 7 are we masking RLRR 3A0 NC RTN no return here RLRR 270 RAMSLCT select bEO bE1 104 CLRF 8 assume LSb is a zero this exits with CY status 038 READATA read initial bEO bE1 transferred to F8 so it ll be 19C PT 11 hot field delimiter possible to adjust later using the C lt gt ST instruction RLRR RLRR RLRR RLRR 3B0 2EA 013 108 po O OAA SEO A lt gt B ALL B A ALL C CANDA CHO PT lt JNC 02 NO skip process SETF 8 yes set F8 for later check RTN mask to A keep maskin B AND the mask c Martin McClure Page 61 of 63 September 2015 HP16C Emulator Module for the HP 41CX To be continued c Martin McClure Page 62 of 63 September 2015 HP16C Emulator Module for the HP 41CX ja D W om Ww amp Ww hh SR EERE S amp S ae Dah aRES Pr ob b amp amp 32 33 39 36 af a9 41 42 43 44 47 49 51 Original Functions BITS 16 16 16 16 16ABS 16CHS 16ENT 16RDN 16RUP 1650RT 16X 07 16X Y 16X lt 0 16X lt 16K lt gt 16X lt 0 16X lt 16M 0 16M 16X20 16X20 1CMIP 2CMP AND ASR BINM CL16X DBL DBL DBLR DECM DSZ FLOAT HEXM ISZ LST16X NOT OcTM OR RL RLC RMD RR RRC SHOW SL SR STATUS UCMIP KOR med om Ww amp w he Modified Functions 16C FAT2 16C STCK HP 16
70. nput 16NPT SHIFT Another usability feature of 16NPT allows you to change the selected base mode on the fly directly from the 16NPT prompt Pressing the SHIFT key will toggle the selected base amongst the four possible ones in the sequence HEX gt OCT gt DEC gt BIN repeated cyclically Note that each time you change the base the contents of ALPHA and FX registers will be reset including the existing partials if previously entered so you ll start the digit entry process from the scratch This ensures that only appropriate characters for the new base are in the FX buffer rejecting previously entered ones before the base change If you cancel the data entry the current value in the 16X register will be shown again in the last base mode selected during the cyclic rotation Quick Entry Shortcut for lower bit values 16NPT RADIX Besides the normal procedure explained before there is a quick entry mode also available for va ues below the 32 bit limit i e only impacting the lower bits half of the 16X register Simply type the floating point BCD value using the standard X register then call L6NPT and hit the radix key decimal point This will call the LOW16 function effectively terminating the entry appending the number in X as data input clearing the higher bits and lifting the 16C stack appropriately The entered value will be shown in the currently selected base mode thus it ll only be e
71. nput function Characters in ALPHA next value entered in 16X 55 16RCL __ Recalls value from memory values in data registers value from memory into 16X 56 16RDN Rolls the 16C stack down values in 16C stack 16C stack rolled down 57 16RUP Rolls the 16C stack Up values in 16C stack 16C stack rolled up 58 16STO __ Stores 16X in memory value in 16X and prompt 16X stored in data registers 59 16X lt gt __ Exchanges the 16X and mem values in 16X and data regs 16X and data regs exchanges 60 16X lt gt Y Swaps 16X and 16Y values in 16X and 16Y 16X and 16Y exchanged 61 CL16X Clears the 16X register anything in 16X 16X is zeroed 62 CL16ST Clears al the 16C stack anything in 16C stack the 16C stack is zeroed 63 LST16X Recalls last value used value in 16L reg pushes 16L into 16X 64 X Y _ XY Tests launcher XY tests launcher executes function O 16C FAT2 Section header section header n a 1 BIT_ Bit Functions Launcher prompts for function executes function 2 XSHF _ Shift Bist Launcher prompts for function executes function 3 XRIGHT _ Right Launcher prompts for function executes function 4 16APN Append String to Value Partial String in Alpha Appends to Exisiting Value 5 16x42 Squares 16X value in 16X result in 16X argument to 16L 6 16X 0 tests 16X equal to zero value in 16X YES NO skips line if false 7 16X 0 tests 16X not equal to zero value in 16X YES NO skips line if false 8 16X lt 0 tests 16X less than zero value in 16X YES NO skips line if false
72. ontent of b13 will be overwritten and in the move case L H the X register will be cleared after the copy A pre requisite for these functions is that the current word size needs to to be larger than 32 in order for the higher bits register to be shown during the masking process If this is not the case the rerror message WS nn will be shown or DATA ERROR in a program execution The schematic below graphically shows the actions performed by these three functions 16 Register m Mreg b13 L H Lon 4 2 3 Doubling and Halving the 16X value 2MLT 2DIV 2DIV and 2MLT Handy shortcuts to divide or multiply the contents of the 16X register by two It saves bytes in a program and keystrokes during manual mode It does not lift the 16C stack but saves the original number in LST16X Note however that the CY and OOR flags are not always set by these functions c Martin McClure Page 42 of 63 September 2015 HP16C Emulator Module for the HP 41CX 4 2 4 Digit Justification Reversal and Decimal Sum DGLJ These functions can be considered an extension of the bit based conterparts LJY REV and BITS The concepts are analogous to the original set but these are digit based instead of bit based The results may be sometimes similar or even the same but in general thay are totally different e DGLJ does a digit based left justification of the value in 16X which in general is not the same as
73. or if DEC mode and the value represents a negative value only occurs in 1 s or 2 s complement mode Similar to the previous one there is also a sub function available to execute the internal routine for diagnostic cases It will assume the information is already in binary format in the EX registers to move it up to the FX registers in ASCII form The hierarchical levels amongst the input registers are shown again in the figure below with the sequence of routines needed to move the data up and down the different stages 16X lt E0 E1 FX2EX A2FX 16NPT 16T 167 167 16X EX Binary NNN FX ASCII ALPHA 16X gt E0 E1 EX2FX SHOW c Martin McClure Page 56 of 63 September 2015 HP16C Emulator Module for the HP 41CX Multiplication routine The multiplication routine covers both 16 and DBL in one routine When the code needs to be specific it uses an internal system flag specifically system flag 5 to perform the unique code for the specific function The beginning of the routine is basically the same 1 16LastX is performed to save the value of buffer 13 and stack register X into buffer 14 and stack register L The binary value of Y and contents of buffer 12 16 multiplier are moved to buffers E2 and E3 The binary value of X and buffer 13 multiplicand are already in EO and El 2 If in 1 s complement or 2 s complement mode take the absolute value of both the multiplicand and the multipl
74. otate ALPHA 29 ABSP remove base id 30 ABSP 31 ABSP 32 RDN chars 33 ALENG ALPHA length 34 STO 00 save for later 39 of zeros of i ie add one 38 DSE X decrease counter 39 GTO 00 do next 40 RCL 00 ALPHA length 41 AROT rotate ALPHA 4 FS 04 Hex 43 J H yes af FS 03 Oct 45 o yes 46 FS 01 Bin 47 j b yes 48 j e append blank 49 3 rotate contents 50 AROT 51 AVIEW show result 52 16RCL 00 recall argument 53 RTN done Decimal 55 16RCL 00 recall argument 56 SHOW show current 57 END As you can see all action happens in the ALPHA register and therefore the usage of the standard X Functions AROT ALENG and ABSP from the OS X module as well Not only this program requires the data registers 16R00 to preserve the original value but it should also be said it will fail in 1 2CMP due to the incompatible usage of user flags 1 and 2 c Martin McClure Page 52 of 63 September 2015 HP16C Emulator Module for the HP 41CX Appendix C Data Buffer Technical Details This document is an attempt to descript the format of the B buffer used by the HP 16 MCODE Emulator Module developed by Angel Martin and Greg McClure The B buffer is used to allow full 64 bit word size emulation as implemented on the HP 16 The buffer requires 20 free registers Function CHKBB check for buffer B is used to check for and create if needed buffer B The format of the buffer from highest absolute register to low
75. overed later in the manual Hopefully you re also intrigued about the new additions to the function set located in the auxiliary FAT and can probably guess their scope and intention that will be the subject of dedicated sections as well as they are likely to add some surprises to the digital mix Refer to the table in next page for a quick comparison between new modified and original functions in the emulator c Martin McClure Page 9 of 63 September 2015 HP16C Emulator Module for the HP 41CX wmd om in amp ww he osu nin Boe eS 19 ai Eome SDAN af a9 41 42 43 45 47 49 51 Original Functions BITS 16 16 16 16 16AB5 16CHS 16ENTA 16RDN 16RUP 1650RT 16X 0 16X Y 16X lt 0 16X lt 16X lt gt 16 lt 0 16X lt Y 16X 0 16M 16X20 16X gt Y 1CMP 2CMP ISZ LST16 4 NWOT OCTM OR RL RLC RMD RR RRC SHOW SL SR STATUS UCMP XOR Pie bb BE S ee so in a w a bk Modified Functions 16C FAT2 16C STCK HP 16C TESTING 16APN 16NPT _ 16RCL__ 165TO _ LDZER LOW16 MASKL _ _ MASKR __ RLCN RLN __ RRCN _ RRN Sb WINDOW _ woo ow oom in b woh oe New Functions BIT _ LEFT _ MOD _ RIGHT _ EROT _ 16C _ 16KEYS _ 16W57 16Kann 16X 2 16X lt gt _ 16X gt 0 16X gt Y 2DIV 2MLT A2EK BASE CHKBB CL165T CLRFX D gt H DGDE DGU DGRV EX2FX FCAT _ FM2EX EMSZ GET16 H L H gt D L lt gt H
76. ponding index Refer to the sub function launchers section for further details on 16 and 16 As a last remark it comes without saying that the characters in ALPHA should conform to the selected base and word size restrictions There won t be any error message if this is not done but as a rule the function will always normalize the input applying the current mask against it in program mode thus possibly changing the input but wrong entry into allowed values Summary of 16NPT hot keys e ENTER terminates the digit entry e R S terminates the digit entry e SST appends digits to buffer and moves to next partial e CHS terminates digit entry and changes the sign e terminates digit entry and does subtraction e terminates digit entry and does addition e terminates digit entry and multiplies by 16Y value e terminates digit entry and divides by 16Y value e SHIFT discards digits and changes base mode on the fly e RADIX discards digits and enters low bits value from X register e BackArrow deletes last digit or cancels out if last one e ALPHA launches the 16 function c Martin McClure Page 15 of 63 September 2015 HP16C Emulator Module for the HP 41CX The 16C Digit Pad and 16C Keyboard Overlay Related to the quick entry modes you can also use the f amp e digit pad to directly enter 1 9 single digits as values This is done from the 16C prompt no need to call 16NPT at all so even if its applica
77. present no sign Negative value flag for Decimal signed modes The XS digit of the FO register has a special function to denote that a negative value is to be presented in the LCD when a signed decimal base mode is the selected one When the value is not zero it will direct the SHOW routine to add a minus sign before the value for the familiar representation convention This is also controlled by the complement mode and built in the EX2FX code feet USER 1 Functions buffer usage outlines The following sections will show how the buffers are used in various math logic programming functions One of the first things that will be noticed is that in addition to the auxiliary E2 and E3 buffer registers for more complex cases buffers FO and F1 are here also used as temporary registers for calculation purposes c Martin McClure Page 55 of 63 September 2015 HP16C Emulator Module for the HP 41CX Input Output Routines Input of various values for calculation is accomplished via several possible routines mentioned in this manual LONPT LOW16 16APN At the core of these functions are the FX2EX and EX2Fx routines which are also available as sub functions that move the results of input back and forth between the FX registers and buffers EO thru E2 The info in buffers FO thru F7 are ASCII values The FX2EX function translates the ASCII codes in buffers FO thru F7 into binary in buffers EO and E1 It relies on the mode
78. qual to the BCD input in decimal mode For example the sequence 12345 LOW16 will return H 3039 c Martin McClure Page 14 of 63 September 2015 HP16C Emulator Module for the HP 41CX Program Mode Operation You re no doubt wondering how the data is input under program control where all the hot keys and Shortcuts are not available The first thing to say is that 16NPT is indeed programmable and that in a running program it takes its input digits from the ALPHA register Therefore this is already good enough to enter any values in Octal Decimal and Hexadecimal modes regardless of the word size selected For binary mode you may need to append more data after the first 24 digits are dealt with this way if the word size is larger than 24 bits as in binary each bit is a full ASCII digit You ll then use the 16APN sub function for that purpose effectively performing the same trick as with the key in manual mode to enter partials As an example let s see two possible ways to input the hexadecimal value 1234ABCD illustrating the usage Of 16NPT and 16APN choices at your disposal 1 Choice only two program lines required 2 Choice it takes four lines to do the same 01 1234ABCD 01 1234 first part break at will 02 16NPT 02 16NPT 03 ABCD second part 04 16APN Note that because 16APN is a sub function the last line in the second choice is really two program lines aS you need function 16 and the corres
79. r the HP 41CX HP IBE Emul ator Module Table of Contents 1 Introduction 1 1 Introduction 5 1 2 Page 4 Library and Bank Switching 5 1 3 Organization of the Manual and Remarks 6 7 1 1 4 Function Index at a glance 1 5 New Original Function Table 0 2 The 16C Data Structure 2 1 The Martin McClure Buffer 11 2 1 1 16C Stack Operation 11 2 1 2 Stack and memory Functions 12 2 2 Data Input with 16NPT 13 2 2 1 The 16C Keyboard and Overlay 16 2 3 Data Output with SHOW and WINDOW 17 2 3 1 The true meaning of GRAD 18 2 3 2 Data Formats Summary 18 3 What s New amp Different 3 1 Differences from the Original 19 3 1 1 Number Entry and FLOAT mode 20 3 1 2 Flags as Semaphores CY and OOR 21 3 1 3 Status and Flashing messages 23 3 1 4 Prompting Functions 24 3 1 5 Test functions launchers 25 3 1 6 ISZ DSZ and function Parameters 26 3 1 7 Square Root and Square power 27 3 1 8 A few examples Gray code bit extraction add w CY 28 3 2 New Functionality added 29 3 2 1 Rotations Launcher 29 3 2 2 Shifting and Bit operations Launcher 29 3 2 3 Bases and Signed Modes Launcher 30 3 2 4 Left and Right Launchers 31 3 2 5 Launcher Shortcuts Map 32 3 3 Remaining Functions not on Launchers 33 3 3 1 Last Function and Programmability 34 c Martin McClure Page 3 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 4 Individual Function descriptions 35 3 4 1 Negative Logic Functions 35 3 4 2 Word size re
80. rs Greg s programming Skills have been put to a good use in the base conversion and big math algorithms which work seamlessly integrated into the module completely behind the scenes The double precision multiplication and division in particular are highlights of the module taking up the third bank in its entirety by themselves which speaks volumes about their intricate design and complex implementation From my part this module brings it all together home in many ways starting with the advanced concepts borrowed from the 41Z Complex module dealing with auxiliary buffers for data storage and abstraction data layers above the native real numbers support on the 41 OS from the SandMath and PowerCL modules pioneering the function Launchers and of course the heavy reuse of Auxiliary FATS and sub function management leveraging the Library 4 design way beyond its initial design scope All in all this module is nothing short of an improbable amazing feat if you ask me and I think I speak on both Greg s and my own behalf to say it s an important contribution to the 41 legacy It has been a very rewarding project and a great learning opportunity for me as well thank goodness Greg was on watch to keep all those whimsical components of the 16C intricacies at bay many times during the development when I was getting completely confused PS The trademark Martin McClure is a result of a virtual coin toss and some consideration
81. ry sake But there s also some slight difference in the way LJY the Left Justify function works The 16C Emulator versions return the left and right justified values to the 16X register and the number of positions needed to do the justification in the 16Y register exactly opposite to the original LJ function on the machine Not much of a difference as executing 16X lt gt Y will bring things back to the original shape but nevertheless important for you to be aware of in case you re using programs copied from the original machine c Martin McClure Page 36 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 4 5 Shifting multiple Positions The original 16C includes one position shifting functions SL and SR which on the emulator have been moved to the Auxiliary FAT as subfunctions Their place in the main FAT has been taken by n position versions of the same functiions which as a particular case can also perform the single position With n 1 The number of positions is entered in the function prompt in manual mode or taken from the 16X register when running a program In a program any value larger than the current word size or zero will result in a DATA ERROR condition but in manual mode e Entering a number larger than 64 will be ignored and the prompt will stay put e Entering a number larger then the word size will show the message WS nn and cancel e Entering zero at the prompt
82. s Taking advantage of the alphanumeric capabilities the complement mode is shown as Oc 1c or 2c Likewise the selected base is spelled out as mnemonic BIN DEC OCT HEX or FLT The text is right justified and will stay in the display for a short while before the current value in the 16X register is shown again The examples above both show the machine recently had both Carry user flag 3 and Out of Range user flag 4 conditions You can see that the complement mode matches the status of flags 0 1 2 Flashing Functions Some functions will flash the result for a while and then revert to showing the current value in the 16C register For STATUS this is also the case on the original 16C and like on it you can hold the flashing display by holding any key after you have allowed it to be presented or otherwise all you ll get is the NULL message from the 41 OS Besides STATUS the other flashing functions are BITS WSFIT and 16WSZ the last two being new additions to the function set which will be described later on New Flashing Error Conditions The Division functions may show the error conditions to denote a math error condition either a division by zero in 16 or a quotient result too large for the selected word size in DBL These error messages will briefly show in the display but the original arguments will remain in the 16C stack If this occurs during a program the execution will halt showing
83. set in buffer register b01 BIN OCT DEC HEX For BIN OCT and HEX modes this is easy It takes the info from each ASCII code in the FO thru F7 buffers and shifting it into buffer EO overflow bumping into buffer E1 In decimal a special multiply by 10 and add value routine is required to perform the translation into binary instead of shifting by 1 BIN 3 OCT or 4 HEX Every math or logic routine will use the info in buffers E1 EO as the 16X argument The result that should be in the 16X argument at the end of the routine is placed into buffers E1 E0 and a routine is called to move that into the 16X register and displayed The internal routine EOQ1OUT is used to do this The EX2FX routine is at the core of this process The display functionality of EQ1OUT is reproduced with the SHOW function EX2FX is the mirror of the FX2EX routine It takes the info in EO and E1 and translates it into buffers FO thru F7 Again it relies on the mode set in buffer 01 BIN OCT DEC HEX For BIN OCT and HEX modes this is straightforward bits are shifted into the buffers and changed into ASCII codes For DEC mode a special routine to divide by 10 also has to be implemented The sign of the decimal value has to be considered as well it is the only mode we have to worry about the sign As digits are found the contents of buffer FO thru F7 are shifted and a proper count is maintained for each buffer Buffer register FO also contains the negative indicat
84. signed to their corresponding keys When executed it prompts for the action to perform press Y N either to do the assignments or to clear them You can also cancel at this point pressign the back arrow key Once the action is completed the function will display the current value in 16X This method removes the need to press the Ma prefix key each time you need to execute the emulator functions thus from that perspective is a faster one and perhaps the closest to the original machine The only requirement is to have mode on and conversely you ll need to turn it OFF when you need to access any of the standard HP 41 functions Another disadvantage is that no other key assignments are compatible with this mode since all keys have a function assigned It however has two important shortcomings e No support for the LASTF facility or the 16 and 16 launchers since it s not possible to assign functions to the PRGM USER or ALPHA keys Note that you can also use the 16C_STACK function or XROM 16 49 to trigger the LASTF functionality It s easy to do with the XROM function in the OS X module Also to overcome this deficiency the 16 function will be assigned to the RADIX key e No support for sub functions from the auxiliary FAT which have been replaced with Te itself so you have a way to invoke them simple repeat the same action which the second time will trigger the 16C variant on that sequence of keystrokes
85. sitive counterparts Examples Here s a table of direct results with ws 32 and 16x 1 16Y 0 NAND NOR XNOR d 4294967295 d 4294967294 d 4294967294 dt o owe paa fea 2CPM 16WSZ is a flashing function that in manual mode shows the current word size briefly on the display and then enters that value in the 16X register peforming a stack lift You can maintain the flashed message up holding any key once it has been shown or itl just NULL itself out WSMAX simply returns to the real X register the maximum value that can be represented with the currently selected word size In math terms this is calculated by the formula Wsmax e ws Ln 2 1 WSFIT will change the selected word size to the needed number of bits to represent the current value in the 16X register This has two possible uses one to downsize the word size in case the value in 16X is smaller than the maximum one i e eliminating thos bits used by the leading zeroes but another one is to increase its size as per the binary value exisiting in the 16X register which in some instances may be a superset of its visual representation made by SHOW and WINDOW Example With ws 32 calculate the square of H 123456 16NPT 123456 16X 2 returns H 66CBOCE4 and sets the OOR flag Pressing WSFIT shows the message WS 41 followed by H 14B66CBOCE4 c Martin McClure Page 35 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 4 3
86. sizes 5 If in 1 s complement or 2 s complement mode take the absolute value of both the dividend and the divisor saving the state of the combined signs in one of the CPU internal registers G in case your curious This process also involves using buffers F2 and F3 6 The partial division process is performed until all of the dividend is used and a final remainder is left in buffers EO and E1 7 Notwithstanding a lot of weird code that checks for overflow or carry flag conditions carry always indicates a remainder is left no carry means no remainder the high order quotient and BCD conversion of the low order quotient is put into either buffer 12 and stack register Y for 16 and RMD or buffer 11 and stack register Z for DBL and DBLR If the remainder was desired RMD or DBLR then buffers E1 and BCD conversion of buffer EO replaces the quotient 8 If 1 s complement or 2 s complement the proper change sign is performed c Martin McClure Page 59 of 63 September 2015 HP16C Emulator Module for the HP 41CX 9 For 16 and RMD one extended stack drop is performed buffers 10 thru 12 are dropped to buffers 11 thru 13 in addition to the standard stack drop For DBL and DBLR TWO extended stack drops are performed Thus the quotient or remainder is now in buffer 13 and stack register X aS well as E1 E0 10 The division routine returns via a routine that translates the values in buffers EO E1 into buffers FO thru F7
87. t amp ouptut sections of this manual Space is at a premium on both ALPHA and the LCD so it didn t seem to be a good idea to use it with non relevant zeros The only logical and needed exception is during the digit input process in 16NPT which allows for the first digit to be a zero You can however use the subfunction LDZER to shows the value in 16X including the leading zeros as a function of the base and the word size Like it is the case in the original machine this functionality is not available in Decimal mode where the actual number of digits depends on the entered values It is also somewhat limited by the maximum length of the ALPHA registers so it s not recommended you use it for long binary values all other cases will fit Examples show the leading zeros for the OCT value 13 with ws 13 then changed to HEX tt EJ EJ Er f EE er E fC USER 2 USER 2 c Martin McClure Page 22 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 3 3 What s the Status The STATUS function is meant to show the current configuration of the emulator settings Like in the original machine the display includes the complement mode and the word size but contrary to it the flags information is replaced with the currently selected base This should not be a shortcoming considering that the status of the relevant system flags 0 4 is always shown in the annunciators section of the LCD display thus they are visible at all time
88. tal facility but just standard real numbers or even no changes to the display at all e A2FX Alpha to FX Registers This function writes the current content of the ALPHA registers M N O P into the buffer FX registers starting at the first available position within the FX set as per the S amp X field information Up to 24 characters can be written using this function but there is no action on the GRAD annunciator in case of overload e CLRFX Clears FX registers A complete clear of all eight FX registers which resets their active contents to zero Register labels will be respected from FO to F7 in nybbles lt 13 12 gt e EX2FX and FX2EX Moving data between EX and FX registers This pair of functions move the data back and forth between the E0 E1 registers in binary form NNN and the FO F7 registers The ASCII digit values in FX are dependent on the current base mode selected Note that even afer executing FX2EX the result will not be placed in the 16C stack that is the buffer register b13 and stack X register e FXSZ FX Registers size This function returns the number of digits currenly used in the FX registers A maximum of 64 digits is returned for BIN mode only sinc each FX register can hold up to eight characters The status of the GRAD annunciator will be lit if greater than 24 In fact this function is like ALENG for ALPHA but excluding the base id and leading blank charac
89. ter The result will be pushed in the 16C stack BFR EBS and brefly shown in a flashing message USER 0 Advanced user s tip Nothing like a comprehensive RAM editor like RAMED in the OS X module for cursory inspections of all the buffer registers in all their g l ory details even editable if you decide to take a walk on the wild side c Martin McClure Page 41 of 63 September 2015 HP16C Emulator Module for the HP 41CX 4 2 2 Buffer Creation and Data Types CHKBB Check and create Buffer Seminal routine accessed by every single one of the module functions use it to create the 16C Data buffer when needed as it is done automatically during the CALC_ON event polling point L lt gt H Swap Lower and Higher bits You can use this function to swap the low and high bits parts of the 16X register In other words the contents of the stack X and buffer b13 registers will be exchanged doing the required conversions as appropriate b13 BIN X and X BCD b13 Example using a word size of 56 enter the hex value 12300000000000 Type L6NPT 123 L lt gt H gt H 12300000000000 If you execute it again you ll get the original 123 input i e the digits will be shifted down H L and L H Copy and Move Lower bits These two complement the swapping functionality and provide ways to copy and move the lower bits art of the 16X register into the higher bits In both cases the previous c
90. ternal chip of the 41C The actual multiply workhorse routine takes a 16 bit multiplier and 16 bit multiplier and yields a 32 bit result This result is then moved or summed into the required locations in buffers EO thru E3 The multiplicand saved in buffers F0 13 and multiplier saved in buffers F1 12 can be represented as hex digit groups as follows FO aaaa bbbb 13 cccc dddd F1 eeee ffff 12 gggg hhhh The 16 cross multiplications are 1 dddd x hhhh into buffer EO moved 2 cccc x hhhh dddd x gggg into low 16 bits of buffer E1 moved and high 16 bits of buffer EO summed 3 bbbb x hhhh cccc x gggg dddd x ffff into buffer E1 summed 4 aaaa x hhhh bbbb x gggg cccc x ffff dddd x eeee into low 16 bits of buffer E2 moved and high 16 bits of buffer E1 summed 5 aaaa x gggg bbbb x ffff cccc x eeee into buffer E2 summed 6 aaaa x ffff bbbb x eeee into low 16 bits of buffer E3 moved and high 16 bits of buffer E2 summed N and finally aaaa x eeee into buffer E3 summed Thus 16 total cross multiplications are performed The last section of the multiply core normalizes buffers EO thru E3 handles carries from EO to E1 El to E2 etc Thus when double multiply is performed with the max word size of 64 bits a full 128 bit result can be calculated Change Sign Routine An important part of both the multiplication and division routines when working in 1 s complement or 2 s complement mode is the subro
91. the bit based function LJY available in the main FAT and in the original 16C Only when the bit density of the leftmost character i e the number of bits per character is complete then both functions will yield the same result Example with ws 32 left justify the value H 123 using bits and digits as criteria ell chad VS COET e DGRV does a full digit reversal i e mirror image based on the information contained in the ALPHA register This should normally be based on the actual value in 16X and therefore it ll return a digit reversed version of the number The result will be normalized to fit within the current ws and complement mode selected The original value is saved in 16L the last 16C register Note that contrary to the bit reversal situation the result here is completely base dependent Also note that Zero chars on the left after reversion will ultimately be ignored Obviously this function is completely equivalent to REV for binary mode since in that case each bit corresponds to one digit as well Examples with ws 32 any complement mode i ia ae DGRV i heed but say now you have ws 8 Pa en DGRV aia e DGD does a decimal digit sum based on the bcd values from 16X independently from the base mode set The decimal result is briefly shown as a flashing message in the display and then it is input in the 16X level in the configured based replacing the original value which goes to the 16L register as well
92. to be that such all other bits are zero and therefore can easily be generated calling LJY on the number 1 or creating a single bit MSKL or also doing a left shifting of ws 1 number of bits with SLN Corner cases involving the MNV Setting ws 32 2CMP let s do some math using the MNV 32 H 80000000 as one of the arguments i e d 2147483648 Multiplying or dividing the MNV by 1 is perhaps an academic discussion but calculating the result poses some challenges to the algorithms The 16C responds the following in 2CMP Division 16NPT 1 LJY 16NPT 0 NOT 16 gt H 0 and OOR Multiplication 16NPT 1 LJY 16NPT 0 NOT 16 gt H 0 and OOR Note that the last one yields a different result from a sign change of the MNV i e both operations are surprisingly not equivalent in this case Is that a picky behavior or is it justified Mathematically speaking multiplying by 1 should be equivalent to doing 16CHS and for the MVN that results in the same MVN not zero OOR But this is not how it works here where the rule for a sign change is invert then add one and not a multiplication by 1 Such is life in the digital world wf Operation O a 2MPony 0o a 1 1C0MPony 0 OO o ACM only 1 O O MNV _ Signed modes ws 1 __MaxVal Unsigned Mode 0O __MaxVal Signed modes 1 DY In 1CMP 0 1 1 CY adding 1 again returns 0 instead of the original
93. tring of letters separated by colons and the selection is made using the initial letter of the function chosen The first two group the signed modes the base modes and other system configuration controls very fundamental part of the system indeed XMOD is assigned to the USER key on the 16C keyboard and shows the following teo screen when called toggled with the Key as usual Unshifted screen Roughly speaking the left half of the LCD is for the base modes Binary Octal Decimal Hex and Floating Point Mode whereas the right half of the LCD is for the signed mode UCMP 1CMP and 2CMP plus the word size setting 1L6WSZE 16WSZ The question mark is for STATUS XMOD MOD __BINM Binary Display UCMP 0 Unsigned Mode OCTM Octal Display 1CMP_ 1 s Complement mode DECM__ Decimal Display 2CMP_ _ 2 s Comipement mode HEXM__ Hexadecimal display 16WSZE__ Sets word size FLOAT Floating Point mode 16WSZ Shows Currentws Separator shows STATUS Shows the Status Shifted sscreen Here too the left part is for general configuration and information functions whilst the right part includes bit and digit reversal and sums plus the three general bit manipulation functions ZBIT BASE Recalls current base REV Bitreversal 16KEYS 16C key assignments DGD Decimal Digit Sum TS L Toggle Silent Loud BIT Bits set LDZER Shows Lea
94. u can also access any of their menu choices by calling them individually using its index or name within the auxiliary FAT as described in the next pages c Martin McClure Page 31 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 2 5 Launcher Maps Navigating the Function Shortcuts A picture is worth ten thousand words c Martin McClure Page 32 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 3 Remaining functions not on Launchers As there are several other functions not included into any launcher one would assume that there must be some other way to access them After all they can also be very useful either in manual mode or included in your program and who knows some of them can even become your very next favorite one Those amongst you familiar with the SandMath or PowerCL modules would already know the answer is in the sub function execute functions which for the 16C Emulator are 16 and 16 There are three ways to execute any sub function by name spelling all letters at the 16 _ prompt For your convenience the ALPHA mode is activated by 16 so you can start spelling the function directly saving another pressing of the ALPHA key like it is needed for COPY for example by its index entering the number at the 16 _ _ _ prompt in decimal the subfunction name is briefly shown in the display when it is entered using its index at this prompt
95. utine CHSUB also used in function 16CHS It basically takes the value in buffer E1 EO and performs a 1 s complement or 2 s complement on it Buffer E1 is then copied to buffer 13 and the BCD of EO is copied to stack register X Such a seemingly simple task has however its quirks as a result of the definition of a value s complement The maximum negative signed value in particular is an interesting boundary that needed to be single cased for this routine to work correctly in 2CMP mode c Martin McClure Page 58 of 63 September 2015 HP16C Emulator Module for the HP 41CX Division routine The division routine actually covers 16 RMD DBL and DBLR in one routine Whether a divisor or remainder is required division must still be performed When the code needs to be specific it uses two internal system flags specifically system flags 0 and 5 to perform the unique code for the specific function Since there is no division instruction for the internal chip of the 41C it was necessary to figure out how to do division of values bigger than the max size of the 41C registers This was accomplished by the method of partial division The core routine used takes a dividend and divisor up to 40 bits and the result yields both a quotient and remainder Partial division takes progressive high order pieces of the dividend and a shortened divisor usually 20 to 24 bits and uses the core routine to yield a partial quotient The full divisor
96. ver important to document the main design criteria applied to the 16C Emulator module and the derived consequences for its use Special attention has been put to the new and additional functions as well as documenting the small differences that may exist in a few functions when compared to their original implementation on the 16C calculator It is expected that the reader be already familiar with the HP 41 environment so as to be comfortable keying instructions and operating the machine A basic knowledge of the 41 system memory structure and programming will be very useful if you also want to use the 16C module functions in your own programs This module employs several powerful concepts also present in other advanced modules such us a secondary FAT to hold auxiliary sub functions several function launchers that group functions and sub functions by related functionality and the LAST Function facility to re execute the last function or sub function called to mention just the most important ones You may be familiar with all these had you already used the SandMath SandMatrix or PowerCL modules You don t need a 41 CL to run this module but obviously its tremendous speed advantage makes it the best possible choice of hardware Some remarks about the implementation Emulating the complete capabilities of the original 16C machine has been a tall order only possible thanks to a fortuitous combination of dedication and skills from both co autho
97. will toggle between these two functions Obviously right shifting more positions than the current number of bits will result in a zero result Not so obvious perhaps is the case of left shifting a number of positions beyond the current word size which will eventually also result in zero once all bits have been moved off the field Notice that when shifting multiple positions the carry flag will reflect the circumstances on the last bit shiting action and thus not a cumulative effect This is consistent with the behavior of the n position rotation functions RLN and RRN Bacause the shifted bits are lost these two functions are not always complementary of one another This is different from the bit rotation functions where the rotated bits are kept within the word and or CY bit just in different positions Note that when entered in a program it is more byte efficent to use the n positions version with the value 1 in the 16X register three bytes instead of using the 16 launcher followed by its sub fuction index four bytes The 16C stack conditions however are different in those two cases so you should choose the better one for your case c Martin McClure Page 37 of 63 September 2015 HP16C Emulator Module for the HP 41CX 3 4 6 Storing the 16C Stack in Extended Memory GET16 You can use sub functions SAVE16 and GET16 to store and retrieve the complete 16C stack plus the auxiliary buffer registers to from
98. y and 4 for OOR obviously those are also shown in the annunciators area of the 41 display so they were the logical choice As to why carry is 3 and not 4 as in the original machine well we went with the rhyme as opposed to the reason this time CY and OOR will be set and cleared during the execution of numerous functions summarized on the table below In general the CY management is identical to the original machine but the Emulator applies a more extensive rule for OOR in that there are additional instances besides the math functions that also modify OOR This prevents confusing interpretations of why is OOR set now as a left over from several operations before In other words the OOR flag is triggered more frequently on the emulator than it is on the original machine like for instance when recalling a number from memory using 16RCL or another 16C stack function 16RDN or similar in the event that the value being placed in the 16X register is too large for the current word size i e the ws had changed since that number was first stored in the other register Note For more on the CY and OOR flags you should also refer to the Diagnostics section for flashing messages on Carry and Out of Range conditions user selectable in a configurable optional mode The table in next page summarizes all functions impacting the status of CY and OOR flags c Martin McClure Page 21 of 63 September 2015 HP16C Emulator Module for the HP 41

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