    Network Working Group                                            A. Katz
    Request for Comments: 798                                            ISI
                                                              September 1981

                  DECODING FACSIMILE DATA FROM THE RAPICOM 450

    I.   Introduction

       This note  describes  the  implementation  of  a  program  to  decode
       facsimile  data from the Rapicom  450 facsimile (fax) machine into an
       ordinary  bitmap.  This bitmap can then be displayed on other devices
       or edited  and then encoded  back into the Rapicom  450  format.   In
       order  to do this,  it  was  necessary  to  understand  the  how  the
       encoding/decoding  process  works  within  the  fax  machine  and  to
       duplicate  that process  in a program.  This algorithm is descibed in
       an article  by Weber  [1] as well as in a memo by Mills [2], however,
       more information  than is presented  in these papers  is necessary to
       successfully decode the data.

       The program  was written  in L10 as a subsystem  of  NLS  running  on
       TOPS20.   The fax machine  is interfaced  to  TOPS20  as  a  terminal
       through a microprocessor-based interface called FAXIE.

       Grateful  acknowledgment  is made to Steve  Treadwell  of  University
       College,  London and Jon Postel of Information Sciences Institute for
       their assistance.

    II.  Interface to TOPS20

       The fax machine  is connected  to a microprocessor-based  unit called
       FAXIE,  designed  and built by Steve Casner  and  Bob  Parker.   More
       detailed  information  can be  found  in  reference  [3].   FAXIE  is
       connected  to TOPS20  over a terminal line, and a program was written
       to read  data  over  this  line and store it in a file.  The decoding
       program reads the fax data from this file.

       The data comes from the fax machine  serially.  FAXIE reads this data
       into an 8-bit shift register  and sends the 8-bit byte  (octet)  over
       the terminal line.  Since the fax machine assigns MARK to logical 0's
       and SPACE to logical  1's  (which  is  backward  from  RS232),  FAXIE
       complements  each bit in the octet.   The data is sent to  TOPS20  in
       octets,  the most significant bit first.  If you read each octet from
       most significant  bit to least significant  bit in  the  order  FAXIE
       sends  the data to TOPS20,  you would be reading the data in the same
       order in comes into FAXIE from the fax machine.

       The standard  for storing  Rapicom 450 Facsimile Data is described in
       RFC 769 [4].   According  to this standard,  each octet  coming  from
       FAXIE must be complemented and inverted (i.e. invert the order of the
       bits in the octet).   Thus,  the receiving  program  did this  before

    Alan R. Katz                                                    [page 1]

    DECODING FACSIMILE DATA                                          RFC 798
    II. Interface to TOPS20

       storing  the data in a file.   When the decoding  program  reads this
       file,  it must invert  and complement  each octet before  reading the
       data.

       Each data block  from the fax machine  is 585 bits long.   The end of
       this  data  is padded  with  7 0's to make  592 bits  or  74  octets.
       According  to RFC 769,  this data is stored  in a file preceded  by a
       length octet and a command octet.  The possible commands are:

          56 (70 octal)--This  is a Set-Up  block  (the first  block  of the
          file, contains information about the fax image)

          57 (71 octal)--This is a data block (the rest of the blocks in the
          file except for the last one)

          58 (72 octal)--End command (the last block of the file)

       The length field tells how many octets in this block and is always 76
       (114 octal) except for the END command which can be 2 (no data).  The
       length and command octets are NOT inverted and complemented.

       Below is a diagram of each block in the file:

          +--------+--------+--------+--------+--------+--------+--------
          | length | command|  data  |  data  |  ...   |        |
          +--------+--------+--------+--------+--------+--------+--------

    III. The Rapicom 450 Encoding Algorithm

       An ordinary  8 1/2"  by 11"  document  is made  up of about 2100 scan
       lines,  each line has 1726 pels (picture  elements)  in it.  Each pel
       can be either black (1) or white (0).

       The Rapicom  450 has three picture  quality  modes.   In fine  detail
       mode,  all of the document  is encoded.   In quality  mode only every
       other  scan line is encoded  and it is intended  that  these  missing
       lines are filled  in on playback  by replicating  the previous  line.
       There is also express mode, where only every third line is encoded.

    [page 2]                                                    Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                     III. The Rapicom 450 Encoding Algorithm

       Data is encoded  two lines at a time, using a special two dimensional
       run-length encoding scheme.  There are 1726 pels on top and 1726 pels
       on the bottom.   Each pair (top-bottom)  of pels is called  a column.
       For  each  of  the  1726  columns  you  can  have  any  one  of  four
       configurations (called states):

                  column
               (top-bottom)        pels         state
               ------------        ----         ------
                   W-W             0,0            0
                   W-B             0,1            1
                   B-W             1,0            2
                   B-B             1,1            3

       The  encoding   algorithm   can  be   described   in   terms   of   a
       non-deterministic finite-state automaton shown in Fig. 1 (after Mills
       [2]).   You start out in a state (0-3) and transform to another state
       by emitting  the appropriate  bits  marked  along  the  arcs  of  the
       diagram.   For example,  suppose  you are in state  1 (WB).  To go to
       state  2 (BW), you would output the bits 101 (binary); to go to state
       0 (WW)  you would output the bits 1000.  Note that the number of bits
       on each transition is variable.

       In states  0 (WW) and 3 (BB), a special run length encoding scheme is
       used.   There are two state variables  associated  with each of these
       states.   One variable  is a run-length  counter and the other is the
       field  length  (in bits)  of this counter.   Upon entry  to either of
       these  two  states,  the  counter  is  initialized  to  zero  and  is
       incremented  for every additional  column  of the same state.  At the
       end of the run,  this counter  is transmitted,  extending  with  high
       order  zeros  if necessary.   If the count  fills up the field, it is
       transmitted,  the field length  is incremented  by one, and the count
       starts  again.   This count  is called  the run length word and it is
       between 2 and 7 bits long.

       For example,  suppose  we are in state  0 (WW) and the run length for
       this state  (refered to as the white run length) is 3.  Suppose there
       are three 0's in a row.  The first 0 was encoded when we came to this
       state,  there  are two more 0's that must be encoded.   Thus we would
       send a 010 (binary).   Similarly, if there are seven 0's in a row, we
       would send a 110, but eight 0's would be sent by 111 followed by 0000
       and the white run length becomes 4.  (Ten 0's would be encoded as 111
       followed by 0010 and the white run length would be 4).

    Alan R. Katz                                                    [page 3]

    DECODING FACSIMILE DATA                                          RFC 798
    III. The Rapicom 450 Encoding Algorithm

                                      0100
                ------------------------>-----------------------------------
                |                                                          |
                |    -------------------<-------------------------------   |
                |   |                  1                               |   |
                |   V                                                  |   |
          ----------------                       -----------------     |   |
          |              |                       |               |     |   |
          |              |          010          |               |     |   |
       |->|      2       |---------------------->|       1       |->|  |   |
       |  |              |                       |               |  |  |   |
      0|  |     B-W      |          101          |      W-B      |  |1 |   |
       |<-|              |<----------------------|               |<-|  |   |
          |              |                       |               |     |   |
          |              |                 ----->|               |     |   |
          ----------------                 |     -----------------     |   |
              |   ^                        |      |     |   ^          |   |
              |   |     ------------>------|      |     |   |          |   |
              |   |     |           1             |     |   |          |   |
              |   |     |                         |     |   |          ^   V
              |   |     |                         |     |   |          |   |
          0111|   |1    |                         | 1000|   |1         |   |
              |   |     |                         |     |   |          |   |
              |   |     |                         |     |   |          |   |
              |   |     |                         |     |   |          |   |
              |   |     |            1011         |     |   |          |   |
              |   |     |    ----------<-----------     |   |          |   |
              V   |     |    |                          V   |          |   |
          ----------------   |                   -----------------     |   |
          |              |<---                   |               |     |   |
          |              |          0            |               |     |   |
          |      3       |<----------------------|       0       |------   |
          |              |                       |               |         |
          |     B-B      |                       |      W-W      |         |
          |              |---------------------->|               |<---------
          |              |          0            |               |
          |              |                       |               |
          ----------------                       -----------------
              |    ^                                   |    ^
              |    |                                   |    |
              ------                                   ------
               run                                      run
                                   Figure 1.
         Non-deterministic finite-state machine diagram for RAPICOM 450

    [page 4]                                                    Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                     III. The Rapicom 450 Encoding Algorithm

       Run length word lengths must be between 2 and 7.  The field length is
       decremented if the run is encoded in one word and:

          1.  If the run length is 3 and the highest order bit is 0.

          2.  Or, if the run length is 4, 5, 6, or 7 and the highest order 2
          bits are 0.

       In addition to all this, there is a special rule to follow if the run
       occupies at least two run words (and can involve incrementing the run
       word  size)  and the run ends  exactly at the end of a scan line.  In
       this case, the last word of the run is tested for decrement as if the
       previous words in the run did not exist.

       An Example:

          To confirm  the reader's  understanding of the encoding procedure,
          suppose  we had the following  portion  of  a  document  (1=black,
          0=white):

             top row:      0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 ...
             bottom row:   1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 ...
             -----------   -------------------------------
             state:        1 3 3 3 3 2 0 0 0 0 0 2 2 1 0 0 ...

          Suppose  also that the black  run field length is 2, the white run
          length  is 3,  and the state  is  1.   (This  example  comes  from
          reference [1].)

          This portion would be encoded as:

             1 1011 11 000 1 0100 100 1 0 010 1000 ...

          NOTE:  It turns out that the Rapicom 450 sends the bits of a field
          in reverse  order.   This will be  discussed  in  the  section  V.
          However,  since each run length  field is sent reversed, the above
          encoded bit pattern would actually be sent as:

             1 1011 11 000 1 0100 001 1 0 010 1000 ...
                                   ^
                                   |-this is actually 100 reversed

    Alan R. Katz                                                    [page 5]

    DECODING FACSIMILE DATA                                          RFC 798
    III. The Rapicom 450 Encoding Algorithm

       Another Example:

          This example  illustrates the rule for decrementing the run length
          word lengths:

             top row:      0 1 1 0 0 1 1 1 1 1 0 0 ...
             bottom row:   1 1 1 1 1 0 1 1 1 1 1 0 ...
             -----------   -----------------------
             state:        1 3 3 1 1 2 3 3 3 3 1 0 ...

          Here, let us suppose that the black run field length is now 4, the
          white is still 3, and the state is 1.

          This portion would be encoded as:

             1 1011 0001 1 1 101 0111 011 1 1000 ...
                      ^                ^
                      |-goes to 3      |-blk cnt goes to 2

          When we reverse  the order of the run fields, the bit pattern that
          is actually sent is:

             1 1011 1000 1 1 101 0111 110 1 1000 ...
                     ^
                     |-this is actually 0001 reversed, etc.

    IV.  The Setup Block and the Data Header

       Each data block from the fax machine is 585 bits long.  The number of
       blocks  in a  picture  is  variable  and  depends  on  the  size  and
       characteristics of the picture.  It should be emphasized that a block
       can end in the middle  of a scan  line of the document.  There can in
       fact be many scan lines in a block.

       The 585 bit data  block  is composed  of a 24 bit sync  code which is
       used to recognize the beginning of a block, a 37 bit header, 512 bits
       of actual data, and a 12 bit CRC checksum:

          ------------------------------------------------------------------
          |  24-bit  |    37-bit   |         512-bit         |    12-bit   |
          |sync code |    header   |           data          |   checksum  |
          ------------------------------------------------------------------

       The number  of useful  data bits is variable and can be between 0 and
       512 (although there are always 512 bits there, some of them are to be
       ignored).  The number of data bits to be used is given in the header.

    [page 6]                                                    Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                     IV. The Setup Block and the Data Header

       The 37 bits of header is composed of:

          ------------------------------------------------------------------
          | 2-bit |5-bit|  10-bit  |   12-bit  |  3-bit   |   3-bit  |2-bit|
          |seq num|flags|data count| x position|black size|white size|state|
          ------------------------------------------------------------------

       An explanation of these fields follows:

          IMPORTANT  NOTE:   Most (but not all)  of these fields are sent by
          the fax machine  in REVERSE  ORDER.  The order of each n-bit field
          must be inverted.

          Sync code

             This is used to synchronize  on each block.   The value of this
             24 bit field is 30474730 octal (not reversed).

          Sequence number

             This number  cycles through 0, 1, 2, 3 for the data blocks.  It
             is 0 for the Set-Up block (not reversed).

          Flags

             Each of these flags are 1 bit wide:

                Run

                   Purpose unknown, it always seems to be 1.

                Cofb

                   Purpose unknown, it always seems to be 0.

                Rpt

                   1 for Set-Up  blocks (which are repeated when coming from
                   the fax machine  though only one of them is transfered by
                   FAXIE  to TOPS20  and stored  in the file) and 0 for data
                   blocks.

                Spare

                   Purpose unknown, doesn't matter.

    Alan R. Katz                                                    [page 7]

    DECODING FACSIMILE DATA                                          RFC 798
    IV. The Setup Block and the Data Header

                Sub

                   1 if this is a Set-Up block.

          Data Count

             Number of useful bits to use out of the 512 data bits.  NOT ALL
             of the 512 data bits are used,  only this number of them.  This
             number can be 0 (usually in one of the first data blocks) which
             means to throw away this block. (This field is reversed!)

          X Position

             Current  position on the scan line, a value between 0 and 1725.
             If this number  is greater  than where the previous  block left
             off,  the intervening  space should be filled with white (0's).
             If this number  is less than where the previous block left off,
             set the X position  to this value  and replace  the  overlapped
             data with the new data from this  block.   If  this  number  is
             greater  than 1726,  ignore  this field and continue from where
             the previous block left off. (This field is reversed!)

          Black Size

             The size of the black  run length  field, must be between 2 and
             7.   This is the correct  value  for the black  size.   It  may
             differ  from what was found  at the end of the previous  block.
             (This field is reversed!)

          White Size

             The size of the white  run length  field, must be between 2 and
             7.   It may differ  from  what  was found  at the  end  of  the
             previous block. (This field is reversed!)

          State

             The current  state.   This is the correct state.  It may differ
             from the state at the end of the previous block. (This field is
             not reversed.)

          Data

             512 bits of the actual  encoding  of the document.   NOT ALL of
             this data is used in general,  only the amount specified by the

    [page 8]                                                    Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                     IV. The Setup Block and the Data Header

             data count.   If this is a set  up  block,  the  data  contains
             information about the type of document (see below).

          Checksum

             CRC  checksum   on   the   entire   block.    Uses   polynomial
             x**12+x**8+x**7+x**5+x**3+1.

       In a setup block, the data portion of the data block consists of:

          -----------------------------------------------------------
          |   6-bit |    5-bit  |   1-bit  |  20-bits  |  480-bits
          |   flags |    spare  |multi page|  of zeros |  1's and 0's
          -----------------------------------------------------------

       Specifically these are:

          6 flags (each are 1 bit):

             Start bit

                Always 0.

             Speed

                Is 1 if express mode.

             Detail

                Is 1 if detail  mode.  (NOTE:  If the Detail and Speed flags
                are both 0, then data is in Quality mode).

             14 inch paper

                is 1 if 14 inch paper length.

             5.5 inch paper

                is 1 if 5.5 inch  paper length.  (NOTE: If the 14 inch and 5
                inch flags are both 0, then paper length is 11 inch).

             paper present

                is 1 if paper is present at scanner (should be always 1).

    Alan R. Katz                                                    [page 9]

    DECODING FACSIMILE DATA                                          RFC 798
    IV. The Setup Block and the Data Header

          Spare:

             These 5 bits can be any value.

          Multi-page:

             1 if multi page mode

          Rest of data of set-up block:

             The above  fields are followed by twenty 0 bits and the rest of
             the 512 bits of the block are alternating 0's and 1's.

       There  are a number of important points to be remembered in regard to
       the header  of a data block.   First  of all,  the  data  count,  the
       x-position, and the black and white run sizes must be read IN REVERSE
       ORDER.   The reason for this is that the fax machine sends these bits
       in reverse  order.  However, the sequence number and the state fields
       ARE NOT REVERSED.  In addition to this, each run field in the data IS
       REVERSED.   This reversing  of  the  bits  in  each  n-bit  field  is
       completely  separate  from the reversing  and complementing  of  each
       octet mentioned earlier.

       Second, only the first n bits, where n is the value of the data count
       field  (remember its reversed!), of the data is valid, the rest is to
       be ignored.  If n is zero, the whole block is to be ignored.

       Third,  if the x position  is beyond where the last block ended, fill
       the space  between  where  the last block  ended  and the  current  x
       postion  with white (0's).  If the x postition is less then where the
       last block ended,  replace  the overlapped  data with the data in the
       new block.   If the x postition  is greater  than 1726, ignore it and
       continue from where the previous block left off.

       Fourth,  the black  size,  white  size  (reversed),  and  state  (not
       reversed!)  given in the header  are the correct  values even if they
       disagree with the end of the previous block.

       Finally,  the sequence  number  (not reversed)  should  count through
       0,1,2,3.  If it does not, a block is missing.

    [page 10]                                                   Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                                   V. The Decoding Algorithm

    V.   The Decoding Algorithm

       Upon first  glance  at the finite  state  diagram in Figure 1, it may
       seem that it would be difficult  to create a decoding procedure.  For
       example,  if you are in the WW state, and the next bit is a 1, how do
       you know  whether to do a transition to WB or BW?  The answer to this
       is to recognize  that every arc out of the BW state begins with 0 and
       every arc out of WB begins with 1.  Thus, if you are in the WW state,
       and the next  bit is 1,  followed  by a 0,  you know  to go to the BW
       state.   If the next bit is 1, followed by a 1, you know to go to the
       WB state.

       In writing  the decoding program it was necessary to have two ways of
       reading the next bit in the data stream.  The first way reads the bit
       and "consumes"  it,  i.e.  increments the bit pointer to point at the
       next bit.   The other  way does not "consume"  it.   Below  are  four
       statements  which show how  to  decode  fax  data.   The  numbers  in
       parentheses  are not to be consumed, that is to say they will be read
       again in making the next transition.

          If I am in state BW (2) and the next bits are:
             0 (0):             go to BW
             0111:              go to BB
             010 (1):           go to WB
             0100:              go to WW

          If I am in state WB (1) and the next bits are:
             1 (1):             go to WB
             1000:              go to WW
             101 (0):           go to BW
             1011:              go to BB

          If I am in state  WW (0),  then  first  go through  the run length
          algorithm, then if the next bits are:
             0:                 go to BB
             1 (0):             go to BW
             1 (1):             go to WB

          If I am in state  BB (3),  then  first  go through  the run length
          algorithm, then if the next bits are:
             0:                 go to WW
             1 (0):             go to BW
             1 (1):             go to  WB

          For the run length  algorithm,  remember, look at the next n bits,
          where  n is the length  of either  the black  or white  run length

    Alan R. Katz                                                   [page 11]

    DECODING FACSIMILE DATA                                          RFC 798
    V. The Decoding Algorithm

          word,  REVERSE  the bits,  and  output  that  many  BB's  or  WW's
          (depending  on whether black or white run).  If the field is full,
          increment  the size of the word, and get that many bits more, i.e.
          get the next n+1 bits,  etc.  Also, the run length word length can
          be decremented according to the rules given in section III.

          You always  go through the run length even if there is only one WW
          or BB, in this case, the run field will be 0.

          Let us look at the first example given in section III.  Suppose we
          want to decode the bits:  110111100010100100100101000...  (we have
          already reversed the run lengths to make things easier).

          We are in state  1 (WB)  and the black run length word length is 2
          and the white  length  is 3.   We get these  initial values either
          from the block header,  or by remembering  them from the  previous
          transitions  if this is not the start  of the block.  According to
          our rules, we would parse this string as follows:

             1(1) 1011 11 000 1(0) 0100 100 1(0) 0(0) 010(1) 1000...

          The numbers  in parentheses  are numbers  that were read  but  not
          "consumed",  thus the next number  in the sequence  is the same as
          the one in parentheses.   First,  we see a 1 and that the next bit
          is a 1,  this  means  that we go to WB.  Then we have a 1011 which
          means  to go to BB.   Then we do a run, we have a 11 followed by a
          000 which  means the black run length gets incremented by 1 (it is
          now 3)  and we get 3 MORE  BB's.   Now we have  a 1 followed  by 0
          which  means  go to BW.   Next a 0100 which is WW.  Then we have a
          run, 100, which means four more WW's.  We keep going like this and
          we get the original  bit pattern  given  in the first  example  of
          section III.

          It is important  to always  start fresh  when  dealing  with  each
          block.   There  are many reasons  for this.   The  first  is  that
          sometimes blocks are dropped, and you can recover from this if you
          resynchronize  at the start of each block.  Also, if at the end of
          the previous  block, there is about to be a transition, instead of
          making  it at the beginning  of the next block,  the  fax  machine
          gives  the new state in the header of the next block and goes from
          there.   Thus it is important to always start at whatever state is
          given  in the header,  and to align  yourself  at  the  current  X
          position given there also.

          Sometimes,  while decoding a block, a bit pattern will occur which

    [page 12]                                                   Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                                   V. The Decoding Algorithm

          does not correspond  to any transition.  If this happens, the rest
          of the block may be bad and should be discarded.

          The decoding  program decodes the fax data block by block until it
          comes to an END command in the data, or runs out of data.

    VI.  Program Performance

       The L10 NLS program takes about two CPU minutes to run on TOPS20 on a
       DEC KL10 to decode the average document in fine detail mode.  In this
       mode,  the picture  is about  1726 by 2100 pels,  and takes about 204
       disk pages to store.

       We have a program  which displays bit maps on an HP graphics terminal
       and have been able to display  portions of documents.  (not all of an
       8.5"  by 11"  document  will fit in the display).   We  can  use  the
       terminal's  zoom capability  to look at very small  portions  of  the
       document.

    Alan R. Katz                                                   [page 13]

    DECODING FACSIMILE DATA                                          RFC 798
    References

    References

       [1]  Weber,  D.  R.,  "An Adaptive  Run Length  Encoding  Algorithm",
       International   Conference   on  Communications,  ICC-75,  IEEE,  San
       Francisco, California, June 1975.

       [2]   Mills,   D.   L.,   "Rapicom   450  Facsimile  Data  Decoding",
       WP2097/MD33E, COMSAT Laboratories, Washington D.C., undated.

       [3]  Casner,  S.  L.,   "Faxie",   ISI Internal Memo, USC/Information
       Sciences Institute, February 1980.

       [4]  Postel,  Jon,  "Rapicom  450 Facsimile  File Format",  RFC  769,
       USC/Information Sciences Institute, September 1980.

    [page 14]                                                   Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                                                    Appendix

    Appendix

       In this appendix  is given  the first portion of the data which comes
       from the fax machine,  this same data in RFC 769 format,  and some of
       this data decoded  into a bitmap.   The data is represented  in octal
       octets.

       The following  is data of the form which comes out of the fax machine
       with length and command octets added:

          114  70 142 171 330  13 377 377 377 371  53 200   0   5 125 125
          125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125
          125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125
          125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125
          125 125 125 125 125 125 125 125 125 121  21 261 114  71 142 171
          330  40   0 102 326 270 152  42  42  44 111   0  42 151 267 122
          366 110 237 102 211 365 111 171 336  51 244 247 377 377 111 362
          177 377 377 377 377 377 377 377 377 376 104 213 241  41 111 377
          111 337 377 377 377 377 377 377 377 377 377 377 377 163 301 361
          377 377 377 377 360 177  12   0 114  71 142 171 330 141 137 177
          377 344  10   0 160  23 301 160 137 376 204 352 135  27 353 264
            0  70 100   7  20  75   0   0   0   0   0 344   0   0   0   0
            0   0   0   0  34 275   0   0   0   0   0   0   0   0   0   0
            0   0   0   0   7  41 310  34 200   0   0 344   0   0   0  71
           13 331 204   0 114  71 142 171 330 241 137  26 302 160   0  16
          100  71   0 370 270 271   0 162   0  71 174 134 100 162   0  34
          234 200 344   7 156 100   1 310  16 107  43 323 263 220 365 313
          327  57 377 325 331  36  56  47 325 324 344   3 227  40  71  35
          200   1 310   1 313 220   0   0   7 241 330   0   0 137 342 200
          114  71 142 171 330 340  77  40 142 160   0   0   0   0 162  71
           73 162 376 276 234 277 376  67 265 301  16  20 171   1 311 313
          346 377 321  75 256 113 245 377 262 160 136 247  13 251 350 374
          270 236 235 217 136 203 220  75 166 166 364 177 305 366  72 107
           63 330 352 345 313 320  71  34 270  46  57   0

       The following is the same data after put into RFC 769 format (with
       each data octet reversed and complemented):

          114  70 271 141 344  57   0   0   0 140  53 376 377 137 125 125
          125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125
          125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125
          125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125
          125 125 125 125 125 125 125 125 125 165 167 162 114  71 271 141
          344 373 377 275 224 342 251 273 273 333 155 377 273 151  22 265
          220 355   6 275 156 120 155 141 204 153 332  32   0   0 155 260
            1   0   0   0   0   0   0   0   0 200 335  56 172 173 155   0

    Alan R. Katz                                                   [page 15]

    DECODING FACSIMILE DATA                                          RFC 798
    Appendix

          155   4   0   0   0   0   0   0   0   0   0   0   0  61 174 160
            0   0   0   0 360   1 257 377 114  71 271 141 344 171   5   1
            0 330 357 377 361  67 174 361   5 200 336 250 105  27  50 322
          377 343 375  37 367 103 377 377 377 377 377 330 377 377 377 377
          377 377 377 377 307 102 377 377 377 377 377 377 377 377 377 377
          377 377 377 377  37 173 354 307 376 377 377 330 377 377 377 143
           57 144 336 377 114  71 271 141 344 172   5 227 274 361 377 217
          375 143 377 340 342 142 377 261 377 143 301 305 375 261 377 307
          306 376 330  37 211 375 177 354 217  35  73  64  62 366 120  54
           24  13   0 124 144 207 213  33 124 324 330  77  26 373 143 107
          376 177 354 177  54 366 377 377  37 172 344 377 377   5 270 376
          114  71 271 141 344 370   3 373 271 361 377 377 377 377 261 143
           43 261 200 202 306   2 200  23 122 174 217 367 141 177 154  54
          230   0 164 103 212  55 132   0 262 361 205  32  57 152 350 300
          342 206 106  16 205  76 366 103 221 221 320   1 134 220 243  35
           63 344 250 130  54 364 143 307 342 233  13 377

       The following is the first part of the expanded bitmap of this data
       (there are about 4 scan lines here, or 2 pairs of scan lines):

          177 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 367 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          337 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 377 377 377 377 377 377 377 377 377
          377 377 377 377 377 377 377 374   0   4 327 377 377 377 377 377
          374 377 356 377 177   0  10   0 201 200   0   0   0   0 100   0
            0   0   0   0   0   0   1 140   0   0   0   0   0   0   0   0
            0   0   0   0   0   0 204  10   0   0  10   0   0   0 100   0
           20  10   7 250   2   0  57 100 100   2 100 100 164   0  20  21
           31 310 153 137 377 377 377 377 177  32 176 344   2 200 216   0
            4   0 240   0   0  14  70   0   0   0   0   0   2  47 137 336
          137 377 377 377 377 375 377 372  20 140  45 376 377 377 377 237
          377 276 357 377 377 377 227 345 314 175  63 215 202   6 347 143
          377 337 376  70 371 370 352 300 213 373 371 377 377 343  73 334
            0 207 315   3  33 111 377 167 337 377   1 323 365 177 377 177
          377 374 377 135 377 377 365  67 343  55 377 377 377 377 357 377
          377 377 377 377 377 377 203 377 236 175 376 236 337 273 347 377

    [page 16]                                                   Alan R. Katz

    RFC 798                                          DECODING FACSIMILE DATA
                                                                    Appendix

          376  77 377 377 377 377 377 377 377 377 377 377 300   0   0   0
          200 102 177 377 277 377 377 377 376 377 366 365 173 302  12   0
           40 200   0   0   0   4 100   0   0   0   0   0   0   2   5 354
            0   0   0   0   0   0   0   0   4   0  10   0   0   0 200  10
           40  20   1   0 100   0 140   0  20 210 101 374   3 200 155 304
            0   6 100 103 376   0 120 121  31 332 243 177 377 377 377 377
          377 233 377 354   0 241 217   1  30   0 240   0   0  12 150 202
           40   0   0   0  62  47 157 376 173 373 377 377 377 377 377 377
           20 141 321 376 377 377 377 327 377 376 377 377 377 377 237 216
          316 375 167 215 202   6 300 143 377 237 374  70 175 330 377 304
          255 373 153 377 377 353 377 104   0 267 315 203  13 311 177 377
          377 377   1 223 367 377 373 167 377 376  77 137 377 345 165  67
           43  51 277 377 277 377 357 377 377 377 373 177 377 377 223 377
          366 175 376 234 377 271 347 377 376 157 377 377 377 377 377 377
          377 377 377 377 340   0   0   0   0   0 177 377  37 377 377 377
          377 376 367 357 272 300   2   0   4   0   0   0   0   0   0   0
            0   0   0   0  20   0   1 144   0   0   0   0   0   0   4   4
            0   0 100   2 100  10 201  10   0  20  75   0   0  40 142   0
            0  74 341 234 103   4 157 300   0   2   0 141 372   0   0  20
           30 376  55 277 177 377 377 367 377 371 376 100  15  61  16 200
           30   0  40   0   0   0 311 200  24   0   0   0  62  55 377 316
          367 347 377 357 377 377 377 377 170 305   5 276 377 377 377 357
          377 377 377 377 377 177 377 377 357 177 377  76 207 246 340 147
          376 336 356  10  17 320 105 235 275 377 377 373 377 347 335 317
           50  77 377 353  75 333 377 377 377 377 363 337 343 277 356 171
            7 357  76 216 377 211 207 176 257 217 377 377 367 357 357 277
          377 357 377 377 377 375 367 377 377 377 377 375 377 377 356 377
          366 377 377 377 377 377 377 377 377 377 377 377 340   0   0   0
            0  44 373 377  77 377 377 177 177 377 377 337 376 170 173   0
            0   0 100   0   1  10   0   0   0   0   0 200 160   0 223 160
          300   0   0   0   0   0   0   6 100 220   0   0 140   4   3  30
          121  20 351 300 206  74 167   0  30  64  41 234 172  30 175 300
            4  32   4 345 367 200 103  60 177 372 177 233 377 377 377 377
          376 125 207 210 233  21 364 361 277   1  50  16 140 120  41 335
          377 306 214  10  67 377 373 377 377 377 377 377 377 367 377 377
          377 363 277 377 377 377 377 377 267 177 377 377 377 377 377 237
          377 377 377  77 377 377 355 373

    Alan R. Katz                                                   [page 17]