VEX Native Parameter Tables
Contents
1. Mark3A and Mark4 are slightly different data Mark4 replacement formats VLBA is non data VLBA replacement format VLBA can write Mark3A and Mark4 formats VLBA_frmtr_sys_trk Formatter system track to be 0 1 34 35 Applicable to VLBA formatter only Specifies written with specified data data to be written to a particular system track formatter outputs Data type to be written to system xtk_parity xtk_parity if cross track parity to be written track specified in Field 1 duplicate duplicate is this track is to duplicate one of the normal data tracks If Field 2 is xtk_parity i 2 10 Limited to specified set of first track s First track of contiguous set of 18 26 tracks covered If Field 2 is xtk_parity 8 16 tracks covered by cross parity If Field 2 is duplicate Will always be home track data is not barrel home track of data to be written rolled to specified system track VLBA _trnsprt_sys_trk Physical system track head to i 0 1 34 35 This is a duplication within the transport itself so be written as a duplicate of includes all barrel roll specified formatter output track recorder input track Formatter output track recorder mare track to be duplicated S2_recording mode S2 recording mode mode 1 RecordingmodeD Recording mode ID ID char See Notes Notes Example 324 27 Example 32427 Vie S2_2. SX2C setup The specification of the standard_procedures for a station relieves the requirement of creating a new set of procedures for an experiment ROLL Block The ROLL block defines the barrel rolling sequence that may be used in VLBA and Mark4 recording systems It is intentionally defined in a very general way but for the most part will probably be confined to a few canned modes The roll sequence is specified with a roll statement for each track participating in the barrel roll plus statements defining the roll period and reinitialization interval values roll Roll on off char ono Optional See Notes 2 Home track int track Track that would be written in the absence of barrel roll Step 0 destination track Track to which home track is written when barrel roll is initialized step 0 Step destination track track Track to which home track is switched on first increment of barrel roll Step 2 destination track track Track to which home track is switched on second increment of barrel roll Track to which home track is switched on last step of barrel roll Returns to Step 0 as next fg Last step EE track in n step sequence Roll increment period in frames dams fo Roll sequence reinitialization real any time Fixed at 2 sec for VLBA period in seconds at recording Mark4 can be specified Notes 1 Barrel roll is confined to tracks 2 33 within a give
3. y wobble SEXPER Block hum Time series of utl utc values Time series of x pole values Time series of y pole values Normally fixed for entire experiment Normally fixed for entire experiment wS Number of points over which interpolation is done Typically 24 hrs Must be num_eop_points values in this statement Units specification may be omitted er first field num_eop_points values in this Units specification may be omitted field num_eop_points values in this Units specification may be omitted field The EXPER block contains general information useful for the success of the VLBI administrative process Field Parameter target_correlator Experiment name char Contact e mail address char Description Type Allowed values Scheduler e mail address Target correlator VLBA VSOP JIVE Haystack etc Typically will be the standard 6 char experiment designator example RDWPS1 Others may be added FREQ Block The FREQ block describes the signal and sampling characteristics the channels recorded on the tape where a channel is defined as a single USB or LSB output from a BBC This includes such information as total RF sky frequency sideband channel bandwidth sampling rate and bits sample The FREQ block does not attempt to describe the recording mode since the same set of channels may be recorded in different recordi
4. Fields 2 and 3 uniquely define a single bitstream Second multiplex track CEECEE Required for fanout 1 to 2 or 1 to 4 Third multiplex track Third multiplex track track track e track Required for fanout 1 to 4 specifies fan out ratio fanin def o def Sub pass umber pass number single char single char By convention uses characters A B C ete eee eee a OE a 12 4 Chan_ID linkword for multiplex char Link to Chan_ID in selected FREQ def bitstream 1 5 sign or magnitude bitstream of char sign Fields 4 and 5 uniquely define the bitstream which Chan_ID mag occupies bit position on the specified track 6 ChanID linkword for multiplex char Fields 6 and 7 required if fanin is 2 to 1 or 4 to 1 bitstream 2 7 sign or magnitude bitstream char sign mag Fields 6 and 7 uniquely define the bitstream which occupies bit position 2 on the specified track 8 ChanID linkword for multiplex char Fields 8 and 9 required if fanin is 4 to 1 bitstream 3 9 sign or magnitude bitstream char sign mag Fields 8 and 9 uniquely define a bitstream which occupies bit position 3 on the specified track 10 ChanID linkword for multiplex char Fields 10 and 11 required if fanin is 4 to 1 bitstream 4 sign or magnitude bitstream char sign mag Fields 10 and 11 uniquely define a bitstream which occupies bit position 4 on the specified track track_frame_format Frame format on tape track Mark3A
5. char i e moves the most structure and usually changes orientation of secondary axes La 2 Secondary axis type if relevant Oooo E antenna motion 1 Axis type char axis type each motion axis May be used to specify pointing sector in SCHED block a length Useful if needed to distinguish particular antenna from site portable antenna for example Typically axis_type az el or axis_type ha dec or axis_type x yns N S orientation axis_type x yew E W orientation etc Pairing of parameters 1 and 2 must make sense see comment immediately above angle 0 deg north south orientation 90 deg east west orientation Must be one ant_motion statement for 2 3 4 5 6 7 BBC Block The BBC block connects physical BBC s to the logical BBC s defined in the FREQ section and also specifies the connection of the BBC to a logical IF Parameter Field Description Type Allowed Units Comments values BBC _assign Logical BBC link with amp link chan_def statement in FREQ ac 2 Physical BBC int Logical IF link with if_def amp link statement in IF block Notes 1 All logical BBC s defined in the selected FREQ def must be present in the selected BBC def but not necessary vice versa 2 The BBC block is ignored by the correlator CLOCK Block The CLOCK section specifies the necessary clock parame
6. sources are either through the so called phase cal outputs of the Mark IV formatter or direct sampler outputs from the VLBA system Mark IV formatter the sampled data from the USB and LSB outputs of each of two selected BBC s can be directed to the phase cal output The data available to the S2 are unformatted 2 bit samples at 32 Msamples sec regardless of the sample rate chosen for output to the Mark IV recording system If we designate the two selected Mark IV BBC s as BBCx and BBCy the Canadian VIA VLBI Interface Adapter implements a fixed mapping to S2 inputs as follows S2 Input Mk4 bit stream Ly sign Ly mag Uy sign Uy mag VLBA samplers The input to the Canadian VIA box may be taken either from BBC s 1 4 or BBC s 5 8 depending on the physical connector to which it is attached The mapping within the VIA is fixed as follows The information in the above tables is taken from the VLBI System Interface Adapter VIA User s Manual Ver 1 3 ISTS SGL October 25 1996 available at ftp s2 sgl ists ca 14
7. Band_ID linkword to selected amp link FREQ def 3 Component flux density real flux densit a E a E 6 Component position ange position angle real angle Component RA offset wrt angle specified source position Component dec offset wrt real angle specified source position Specifies coordinate system in which For source_type earth_satellite TRACKS Block The TRACKS block defines the various multiplex fan in and fan out modes that can be used to record data on the Mark3A Mark4 and VLBA DAS s In cases where a mode uses fewer than the full number of heads in a single pass alphabetical sub passes are defined tape passes with the headstacks in a fixed position For purposes of multiplex definitions the sample data from each channel are separated into a sign bitstream and for 2 bit sampling a magnitude bitstream The fan out modes single bitstream to 1 2 or 4 tracks are defined with a set of fanout_def statements one such statement for each bitstream and subpass which defines the destination tracks and bit ordering among the tracks In this way a complete definition of the multiplex format is specified The ChanID linkword in each fanout_def statement connects a particular bitstream to the selected def in the FREQ block The fan in modes 1 2 or 4 bitstreams to a single track are defined by a set of fanin_def statements Each suc
8. VEX Parameter Tables Rev 1 5b1 29 January 2002 Each VEX primitive block is allowed to specify only parameters which are defined for that type of block The VEX Parameter Tables define in detail these parameters for each type of block Each table lists the allowed parameter names and the associated fields Field numbers in parenthesis are optional Parameter type amp link is a VEX linkword as defined in the VEX documentation If units are specified the field must have a units label of the proper type units enclosed in parenthesis are assumed and should not be labeled Not all parameters need to be specified for a given experiment only those which are relevant This listing does not attempt to specify the set of relevant parameters but is instead left to the assumed expertise of the scheduling software writer This listing is not to be regarded as necessarily complete either with regard to blocks or the set of native parameters within the blocks Many blocks particularly the XXXX_OBS blocks are not yet specified These block will be defined in the near future Additional parameters will undoubtedly be added as the need arises SANTENNA Block The ANTENNA block specifies the detailed characteristics of the antenna itself including the type of mount and pointing characteristics Parameter Field Description Type Allowed Units Comments values ae eee E axis_type 1 Primary axis type
9. aneously recording headstacks on 2 drives e g VLBA with 2 drives must have two headstack statements with a different headstack and logical drive linkword The headstack s must correspond to the headstack s in the STRACKS block 4 The recording system_ID identifies the particular DAS used akin to a serial number which is usually written in the aux data field of the recorded data The recording system_ID of each DAS within a given type i e Mark4 VLBA K4 etc must be different for each DAS within an experiment the recording system _ID of a particular DAS is usually assigned at the time of 3 manufacture The recording system ID can be used by the correlator to positively identify the particular DAS upon which a tape was written The parameter electronics rack ID is similar parameter except that one and only one of the 5 Iftwo or more antennas share the same DAS the STATION defs for the corresponding antennas must have refs to exactly the same set of DAS keywords including particularly the recording system _ID stations must declare itself as the tape control master with the inclusion of a tape_control master statement within the referenced DAS defs for that station EOP Block The EOP block specifies the earth orientation parameter to be used by the correlator not needed for scheduling or data taking Parameter Field Description Type Allowed values
10. char slp ep Mbps Relevant only for S2 Number of S2 cassettes int 1 8 Must be consistent with total date rate each S2 cassette records 16 Mbps within an experiment This information is often recorded on tape and used at the correlator Recording transport name char S 1 Electronics rack serial number int P tape_motion 1 Specifies how tape is to be char start amp stop controlled continuous adaptive ee SS Minimum gap for stopping tape Notes 1 The DAS parameters are intended to be sufficient to describe any of the many variants of Mark3A Mark4 Mark5 and VLBA 2 For Mark IIIA Mark IV VLBA and Mark 5A systems the headstack statement indicates which headstack outputs from the formatter are connected to the recording system s There must be one headstack statement for each formatter headstack in SCHED block to determine physical drive record_density Tape length length For Mark IA Mark IV VLBA actual tape in field 2 recording system_ID 1 Recording system serial number int Must be unique for each system of a given type See Notes below 1 Define master station in cluster char systems currently deployed Additional parameters may have to be added in the future as systems evolve output to be recorded Multiple recording systems may be connected to a single formatter 3 Ifmultiple headstacks on same drive each headstack must have a different headstack e g Mark IV Systems with multiple simult
11. data_source Define S2 data source aE Relevant for S2 only VLBA_BBC_1 4 VLBA_BBC_5 8 Define BBCx selection from amp link For Mark IV only Link to BBC_ID in FREQ Mark 4 formatter See Notes 3 Define BBCy selection from amp link For Mark IV only Link to BBC_ID in FREQ Mark 4 formatter See Notes Notes 1 Reference to Mark IV Memo 230 aka VLBA Acquisition Memo 393 may help to clarify the details of multiplex and signal switching in the Mark IV and VLBA systems 2 The actual fanin fanout ratio is implied by the number of subfields in the fanout_def or fanin def statements as indicated in the above table 13 For a fanin fanout ratio of 1 to 1 i e one bitstream to one track either fanout_def or fanin def statements may be used Cross track parity is computed after barrel rolling as the last step before writing to tape 5 The S2 recording mode parameter specifies the recording mode to which the S2 system is to be set The available modes are documented in S2 RT User s Manual Version 3 0 162 October 1996 ISTS SGL TR96 033 available at ftp s2 sgl ists ca The selected mode defines the number of recording groups and recorded inputs The S2_group_order parameter in the PASS_ORDER section specifies the order in which the groups are to be recorded 6 The S2 data source parameter specifies the origin of the sampled data recorded by the S2 recording system Typical data
12. el zen_atmos ocean_load_vert 1 1 inclination O pee a e CO a a S E a C a anos o fe a man o f e C fe Ernos fa aa SOURCE Block The SOURCE block defines the sources to be observed and specifies their relevant characteristics particularly position A single source is defined in each def block A crude source model may be specified for each observed Band_ID specified in the FREQ block for purposes of auto scheduling primarily geodesy position of object will be specified source_type 1 Generic source type char star earth_satellite Other types may be added 2 Experiment source type char target dummy may be declared if the source if calibrator specified for pointing purposes only dummy Station field system may use this information source_name 1 Source name char lt 16 char Typically same as def label name e g 3C273B For source_type star em o ooe O o o O oneone orenat a iaa T ror ee ora Se Source position reference frame char B1950 J2000 ref_coord_ frame ra_rate 1 RA proper motion E Typically asec yr Nis Bie source position source position epoch 1 Epoch ofstated position of stated position epoch Needed Needed only if non zero ra_rate or dec_rate if non zero ra_rate or dec_rate source _model Component number One source_model statement for each major source component for each Band_ID link to the selected FREQ def 2
13. ers relevant to various procedures at an observing station Timing parameters are to be used as constraints to the scheduling program The set of timing parameters listed is for the NASA sked program Other scheduling programs may use these and or other parameters Field Description Type Allowed Units Comments values 1 Tape change time Required parameter Time to complete headstack time Required parameter motion Parameter tape_change headstack_motion new_source_command Time to initiate pointing to new real time Required parameter source er ee onloff Optional procedure re onloff Optional procedure new_tape_ setup setup_always parity_check tape_prepass Time needed to do tape prepass reat Pre observation calibration Optional calibration procedure preob_cal Time needed for procedure Mod observation calibration Optional calibration procedure midob_cal Optional calibration procedure Procedure name Specify standard procedure library Specifies that a standard procedure library is to be used 2 3 2 3 postob_cal 2 3 1 1 1 procedure _name_prefix Notes The procedure_name_prefix parameter is intended to allow the specification of frequently used procedure libraries that individual stations may have honed to their particular requirements For instance the geodesy community frequently uses the same station setup over and over again e g so called
14. geodesy length tape_usage_sync Synchronize tape usage Type or optimization for auto scheduling Sliding window for optimization sky_coverage for geodesy covariance sked_optimize window maximize _num_obs Maximum total of observations ono Primarily for geodesy SEFD Block The optional SEFD block allows the sensitivity of each IF to be modeled and used for a crude calculation of expected SNR when used with specified observing modes an d scan length times For geodesy these calculations can be used to automatically adjust scan times for minimum acceptable SNR in order to densify the schedule as much as possible The particular SEFD model to be used can be specified along with the model parameters values sefd_model SEFD model name Shaffer Models may be added sefd IF_ID linkword Patink TY Link to IF_ID in selected IF def real 2 Zenith SEFD flux density SITE Block The SITE block describes the location of an antenna and may be either earth based or earth orbiting Horizon masks for earth based sites may be specified as an aid in scheduling Type of site char fixed earth_orbit Standardized 2 char site name char oa EA ES site_position_epoch site_position_ref site_velocity List of azimuth values Units specification may be omitted after first corresponding to values in field horizon_map_el specified in horizon_map_az fs horizon_map_az horizon_map_
15. h statement defines the bitstreams written to a single track in a specified subpass The set of ChanID linkwords in each fanin_def statement connects the particular bitstreams to the selected def in the FREQ block and specifies their multiplex order on the track Within each fanout_def or fanin_def statement is a field which specifies the sub pass to which it applies A subpass is defined as a single tape pass for which the headstack s s are held at a fixed position Typically for example 16 of 32 tracks may be written in a single tape pass for this case there are 2 sub passes with a given headstack position By convention the subpasses are labeled A B C etc Note that except for the VLBA _trnsprt_sys_trk statement all references to track numbers in the TRACKS block are more properly labeled as home tracks since barrel rolling in the formatter Mark 4 and VLBA and track switching within the recorder VLBA only may lead to modified physical track assignments Normally the actual physical track numbers pre barrel rolled correspond identically to home track numbers values _ def ie ID char single char One fanout_def statement required for each bitstream By convention subpass_ID uses characters A B C etc Null for Mark 5A Chan ID linkword e ID linkword char Link to Chan_ID in selected FREQ def Sign or magnitude bitstream
16. input leading to designations AN AE BN BE CN CE DN DE For the Mark III system IF s 1 2 3 may each be selected with either a Normal or Alternate input leading to the designations 1N 1A 2N 2A 3N 3A PASS_ORDER Block The PASS_ ORDER block defines pass and group ordering relevant for Mark IIIA Mark IV VLBA and S2 systems For Mark IIIA Mark IV and VLBA system each pass is defined by a two part field composed of a numeric headstack position reference defined in the selected HEAD_ POS def followed by an alphabetic subpass identifier defined in the selected TRACKS def example 2A For S2 the S2_group_order statement defines the order of usage of tape groups Parameter Field Description Type Allowed Units Comments values pass_ order First pass ID char e g 1A First pass assumed to be in forward direction For S2 specified group EENE _group_order First group se ae order in which S2 groups are to be recorded Second group number Second group number number Notes 1 The number of fields present in the pass_order or S2_group_order statements specifies the number of tape passes or groups Number of cassettes per group is defined by recording mode specified in TRACKS section S2 groups are numbered starting at 0 2 First pass is assumed to be in the forward ta
17. n headstack For cases of barrel roll using multiple headstacks the roll sequence definition must include all headstacks roll_inc_period roll_reinit_period Barrel roll is applied in the formatter as the last step before the data are written to tape 3 System tracks do not participate in barrel roll The number of fields in the roll statements defines number of positions in the roll sequence All roll statements must specify the same number of positions in the roll sequence 5 Note that all track references elsewhere in the VEX file are to the home track 6 roll off is default Presence of any roll_def statements implies roll on SCHEDULING_ PARAMS Block The SCHEDULING PARMS block specifies various parameters needed for the scheduling program Since each scheduling program may have its own unique set of parameters the S CHEDULING_ PARAMS block is specified strictly as a literal block which must be parsed and interpreted by the relevant scheduling program The parameters listed are some of those for the current version of the NASA sked program Other scheduling programs may use these and or other parameters Note These a are Se only values a a mutual_vis Force all stations to see source all subnet or allow subnet N low_SNR_ reject Reject stations if SNR too low Primarily for geodesy variable _scan_length Use SNR calculation to set scan Primarily for
18. n i range of Required only if headstack 2 is being used headstack motion Headstack 3 position i range of Required only if headstack 3 is being used headstack motion Headstack 4 position i range of Required only if headstack 4 is being used headstack motion IF Block The IF block defines the IF bands used in the observations and is linked to the BBC block which specifies the detailed BBC to IF connections An if _def statement must be defined for each of the IF links specified in the selected BBC def Parameter Field Description Type Allowed Units Comments values IF_ID link word amp link One if_def statement must be present for each separate IF Physical IF name char System dependent Used to create procedures to select proper IF See Notes a a a eR Total effective LO of IF just real freq Positive number before signal enters BBC Phase cal frequency interval real a 1 MHz Null or omission indicates no phase cal Phase cal base frequency Usually 0 in which case may be null or omitted 1 The total effective LO is used in conjunction with the total sky frequency specified for each channel in the FREQ block to calculate the local oscillator setting in each individual BBC 2 The Physical IF Name is a system dependent designation specifying which IF is selected For the VLBA system IF s A B C D may each be selected with either a Normal or External
19. ng modes or on different equipment at different stations Each frequency channel is defined by a chan def statement with at least 8 fields in each statement The capability of specifying frequency switching is also built into the chan_def statement by assigning each frequency channel to one or more numbered states The switching cycle statement then specifies the length of time spent in each of the states Band_ID RF band name TOE ee RF sky frequency at 0Hz in the BBC output Net sideband of this BBC channel Link to selected SOURCE def where it may be used to describe source structure characteristics for scheduling purposes May be omitted if not relevant This frequency in combination with the LO frequency specified in the IF block allows computation of the BBC LO frequency for this channel Note that this will be opposite the labeling on the BBC itself if the IF going into the BBC is net LSB Chan_ID Logical channel name BBC_ID Logical BBC name State 1 period Phase cal_ID Logical phase cal name Frequency switched state numbers in which this channel is active switching cycle Phasing of frequency switch cycle wrt_obs_start wrt_min_mark Notes 1 There must be one chan_def statement for each BBC channel to be recorded Must be different for each channel Used as link to selected TRACKS def Link to selected BBC def where co
20. nnection to physical BBC is made Link to selected PHASE_CAL def block to specify details of phase cal tone s Null specifies no phase cal to be detected Used only with frequency switching Specified state numbers are separated by colons States must be ordered 1 2 Relevant only if frequency switching being used Timing of switching cycle begins according to this specification P time Interval over which state 1 is active State 2 period etc pret time Interval over which state 2 is active etc sample Ignored for S2 rate 2 Ifone or more stations in an experiment observe different sets of frequency channels there must be a separate def for each different set of channels 3 A resolved link must exist for every specified linkword in each chan_def statement HEAD_POS Block The HEAD POS block defines the headstack positioning as a function of headstack position reference number for Mark IITA Mark IV and VLBA systems the HEAD_POS block is irrelevant for other types of recording systems One headstack_pos statement is required for each potential headstack position or set of positions if multiple simultaneous recording headstacks Parameter Field Description Allowed Units Comments values headstack_pos Position reference number TE Headstack 1 position range of length a range depends on system but is typically headstack 1000 to 1000 um motion Headstack 2 positio
21. pe motion direction Mark IHA Mark IV VLBA PHASE CAL _ DETECT Block The PHASE CAL DETECT block is used to specify the phase cal tones to be detected at the observing station Parameter Field Description Type Allowed Units Comments values phase_cal_detect 1 peal_ID amp link Links to a chan_def statement in selected FREQ def Tone number from DC edge of Tone number of first tone to be detected BBC output See tone number definition in Notes ion Tone Tone number o ooo o Tone number of second tone to be detected Note 1 The actual phase cal frequencies are determined by the LO frequencies specified in the IF and FREQ blocks 2 The phase cal frequency spacing are specified in the IF block 3 Tone number is defined as first tone above 0Hz in the BBC output channel etc Phase cal detection will be done on the set of specified tone s which are listed in order of preference in case more tones are specified than can be detected by the hardware The tones are numbered positively from the low DC edge of the BBC output band with tone number 1 being the first tone above DC Tones may also be specified as negative numbers corresponding to their position from the nominal bandedge with tone number 1 being the first tone below nominal bandedge A tone number of 0 specifies state counting rather than phase cal detection should take place PROCEDURES Block The PROCEDURES block specifies paramet
22. r of tape drives transports A Number of physical drives connected to system Specifies correspondence between physical headstack and logical drive Relevant for MkIIIA MkIV VLBA Mark 5A Headstack Headstack function read write read write Drive number offset with which this headstack is associated 2 3 record_transport_name Identifies a particular recording transport Mostly useful for transportable recording systems Identifies particular electronics rack Like a serial number but a name Relevant on for start amp stop and adaptive motion specifies how soon tape should start before expected good data Relevant for S2 only Specifies length of time tape should continue running after end of valid data Typically 0 5 minutes 2 3 4 Relevant for S2 only Specifies minimum valid data time gap during which tape will be stopped Typically 3 minutes Relevant only in antenna cluster where data from more than one station is recorded on a single recording system Defines which antenna controls tape motion Others are assumed to be slaves Added to drive specified in station statement Normally 0 for single drive systems Longitudinal bit density along i bpi Usually 33 333 or 56 000 bpi unit is assumed track Used to compute tape speed Relevant only for MkII MkIV VLBA systems tape_length time length For S2 K4 recording time at data rate specified o S2 tape speed
23. ters for proper correlation of the data Normally this information will be taken from the station logs transcribed manually or as a last resort determined from a fringe search at the correlator Obviously the CLOCK section is needed only by the correlator Parameter Field Description Type Allowed Units Comments values clock_early 1 Starting epoch for validity of this epoch epoch Model in this statement assumed valid until next clock model specified epoch if any May be null of model is valid for entire experiment al clock_early offset of formatter real time gt 0 for formatter tick early te tick with respect to UTC 3 Epoch of origin of clock model of origin of clock model epoch Needed if clock rate or acceleration specified H i ne Hakika time Note In case of clock breaks where multiple sets of clock parameters must be specified for a station during a single experiment multiple clock statements may be used each specifying the starting epoch of validity for the model in the corresponding statement DAS Block The DAS block is intended to define the recording hardware present at a station Because of the many combinations possible various elements of the hardware are separately specified record_transport_type 1 Transport type char Mark3 A Mark4 Additional types may be added VLBA VLBAG S2 K4 Mark5A electronics_rack_type Type of electronics rack Mark3A Mark4 VLBA VLBAG S2 K4 Numbe
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