Bioctal: Hexadecimal 2.0

Independent Submission                                          M. Breen
Request for Comments: 9226                                    mbreen.com
Category: Experimental                                      1 April 2022
ISSN: 2070-1721


                        Bioctal: Hexadecimal 2.0

Abstract

   The prevailing hexadecimal system was chosen for congruence with
   groups of four binary digits, but its design exhibits an indifference
   to cognitive factors.  An alternative is introduced that is designed
   to reduce brain cycles in cases where a hexadecimal number should be
   readily convertible to binary by a human being.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for examination, experimental implementation, and
   evaluation.

   This document defines an Experimental Protocol for the Internet
   community.  This is a contribution to the RFC Series, independently
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   document at its discretion and makes no statement about its value for
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   see Section 2 of RFC 7841.

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Table of Contents

   1.  Introduction
     1.1.  The Pernicious Advance of Hexadecimal
     1.2.  Problems with Hexadecimal
     1.3.  Other Proposals
   2.  Bioctal
   3.  Objections to Be Dismissed
   4.  Security Considerations
   5.  IANA Considerations
   6.  Conclusion
   7.  Informative References
   Acknowledgments
   Author's Address

1.  Introduction

1.1.  The Pernicious Advance of Hexadecimal

   Octal has long been used to represent groups of three binary digits
   as single characters, and that system has the considerable merit of
   not requiring any digits other than those already familiar from
   decimal numbers.  Unfortunately, the increasing use of 16-bit
   machines and other machines that have word lengths that are evenly
   divisible by four (but not by three) has led to the widespread
   adoption of hexadecimal.  Table 1 presents the digits of the
   hexadecimal alphabet.

                              +=======+=======+
                              | Value | Digit |
                              +=======+=======+
                              |     0 | 0     |
                              +-------+-------+
                              |     1 | 1     |
                              +-------+-------+
                              |     2 | 2     |
                              +-------+-------+
                              |     3 | 3     |
                              +-------+-------+
                              |     4 | 4     |
                              +-------+-------+
                              |     5 | 5     |
                              +-------+-------+
                              |     6 | 6     |
                              +-------+-------+
                              |     7 | 7     |
                              +-------+-------+
                              |     8 | 8     |
                              +-------+-------+
                              |     9 | 9     |
                              +-------+-------+
                              |    10 | A     |
                              +-------+-------+
                              |    11 | B     |
                              +-------+-------+
                              |    12 | C     |
                              +-------+-------+
                              |    13 | D     |
                              +-------+-------+
                              |    14 | E     |
                              +-------+-------+
                              |    15 | F     |
                              +-------+-------+

                                 Table 1: The
                             Hexadecimal Alphabet

   The choice of alphabet is clearly arbitrary: On the exhaustion of the
   decimal digits, the first letters of the Latin alphabet are used in
   sequence for the remaining hexadecimal digits.  An arbitrary alphabet
   may be acceptable on an interim or experimental basis.  However,
   given the diminishing likelihood of a return to 18-bit computing, a
   review of this choice of alphabet is merited before its use, like
   that of the QWERTY keyboard, becomes too deeply established to permit
   the easy adoption of a more logical alternative.

1.2.  Problems with Hexadecimal

   One problem with the hexadecimal alphabet is well known: It contains
   two vowels, and numbers expressed in hexadecimal have been found to
   collide with words offensive to vegetarians and other groups.

   Imposing a greater constraint on the solution space, however, is the
   difficulty of mentally converting a number expressed in hexadecimal
   to (or from) binary.  Consider the hexadecimal digit 'D', for
   example.  First, one must remember that 'D' represents a value of 13
   -- and, while it may be easy to recall that 'F' is 15 with all bits
   set, for digits in the middle of the non-decimal range, such as 'C'
   and 'D', one may resort to counting ("A is ten, B is eleven, ...").
   Next, one must subtract eight from that number to arrive at a number
   that is in the octal range.  Thus, the benefit of representing one
   additional bit incurs the cost of two additional mental operations
   before one arrives at the position where the task that remains
   reduces to the difficulty of converting the remaining three digits to
   binary.

   These mental steps are not difficult per se, since a child could do
   them, but if it is possible to avoid employing children, then it
   should be avoided.  An appeal to the authority of cognitive
   psychology is perhaps also due here, in particular to the "seven plus
   or minus two" principle [Miller] -- either because octal is within
   the upper end of that range (nine) and hexadecimal is not, or else
   because the difference in the size of the alphabets is greater than
   the lower end of that range (five).  Either way, it is almost
   certainly relevant.

1.3.  Other Proposals

   Various alternatives have already been suggested.  Some of these are
   equally arbitrary, e.g., in selecting the last six letters of the
   Latin alphabet rather than the first six letters.

   The scheme that comes closest to solving the main problem to date is
   described by Bruce A. Martin [Martin] who proposes new characters for
   the entire octal alphabet.  While his principal motivation is to
   distinguish hexadecimal numbers from decimals, the design of each
   character uses horizontal lines to directly represent the "ones" of
   the corresponding binary number, making mental translation to binary
   a trivial task.

   Unfortunately for this and other proposals involving new symbols,
   proposals to change the US-ASCII character set [USASCII] might no
   longer be accepted.  Also, it seems unrealistic to expect keyboards
   or printer type elements (whether of the golf ball or daisy wheel
   kind) to be replaced to accommodate new character designs.

2.  Bioctal

   Table 2 presents the hexadecimal alphabet once again, this time in a
   sequence of two octaves with values increasing left to right and top
   to bottom.

                     +---+---+---+---+---+---+---+---+
                     | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
                     +---+---+---+---+---+---+---+---+
                     | 8 | 9 | A | B | C | D | E | F |
                     +---+---+---+---+---+---+---+---+

                          Table 2: The Hexadecimal
                           Alphabet in Sequential
                                  Octaves

   Arranged thus, the binary representation of each digit in the second
   octave is the same as the digit above it, but with the most
   significant of the four bits set to '1' instead of '0'.

   The incongruity of two decimal digits in the second octave also
   suggests that, in blindly aligning with four bits, hexadecimal (six
   plus ten, neither of which are powers of two) misses an opportunity
   to align also with three bits.

   Bioctal restores congruence by replacing the second row with
   characters mnemonically related to the corresponding character in the
   first octave.

   Table 3 shows the compelling result.

                     +---+---+---+---+---+---+---+---+
                     | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
                     +---+---+---+---+---+---+---+---+
                     | c | j | z | w | f | s | b | v |
                     +---+---+---+---+---+---+---+---+

                            Table 3: Bioctal in
                             Sequential Octaves

   The mnemonic basis is the shape of the lowercase character.  This is
   seen directly for '2', '5', and '6'.  For '3', '4', and '7', the
   corresponding letters are the result of a quarter-turn clockwise
   (assuming an "open" '4').  The choice of 'c' and 'j' for '0' and '1'
   avoids vowels and lowercase 'L', the latter being confusable with '1'
   in some fonts.

   With this choice of letters, it is immediately evident that both
   problems with hexadecimal are solved.  Mental conversion is now
   straightforward: if the digit is a letter, then the most significant
   of the four binary bits is '1', and the remaining three bits are the
   same as for the Arabic numeral with the same shape in the first
   octave.

3.  Objections to Be Dismissed

   Several objections can be anticipated, the first of which concerns
   the name.  The term "bioctal" is already used to refer to the
   combination of two octal characters into a single field on, for
   example, paper tape (e.g., [UNIVAC]).  However, if the word "bioctal"
   must be disadvantaged relative to words such as "biannual" in the
   number of meanings it is allowed to have, then it is the paper tapers
   who must give way: in that context, the "octal" part of "bioctal"
   refers to the number of distinct values that three bits can have,
   while the "bi" refers to a doubling of the number of bits, not
   values.  A meaning depending on such a discordant etymology does not
   deserve to endure.

   Second, it may be argued that the use of hexadecimal has already
   become too entrenched to be changed in the short term: Bioctal should
   be introduced only after those working in the industry who have grown
   accustomed to hexadecimal have retired.  Such a dilatory contention
   cannot be allowed to impede the march of progress.  Instead, any data
   entry technician who claims to have difficulty with bioctal may be
   reassigned to duties involving only binary numbers.

   A third possible objection is that numbers in bioctal do not sort
   numerically.  However, this assumes a sort based on the US-ASCII
   order of symbols; it is quite possible that bioctal numbers sort
   naturally in some lesser known variety of EBCDIC.  Further,
   resistance to numeric sorting may be an indicator of virtue, being
   suggestive of an alphabet with a certain strength of character.

   One difficulty remains: Not all computers support lowercase letters.
   While this is indeed true, it should be confirmed in any particular
   instance: the author has observed that in many cases a machine having
   a keyboard with buttons marked only with uppercase letters also
   supports lowercase letters.  In any case, it is permissible to use
   uppercase letters instead of the lowercase ones of Table 3; the
   morphology mnemonic continues to work for most bioctal digits in
   uppercase, although an extra mental cycle is required for 'B'.

4.  Security Considerations

   The letters 'b' and 'f' appear in both the bioctal and hexadecimal
   alphabets, which makes potential misinterpretation a concern.  A case
   of particular hazard arises where two embedded systems engineers work
   to develop a miniature lizard detector designed to be worn like a
   wristwatch.  One engineer works on the lizard proximity sensor and
   the other on a minimal two-character display.  The interface between
   the circuits is 14 bits.  To make things easier, the engineer working
   on the display arranges for these bits to be set in a pattern that
   allows them to be used directly as two seven-bit US-ASCII characters
   indicating the most significant lacertilian species detected in the
   vicinity of the device.  Due to the use of an old US-ASCII table
   (i.e., one in hex, not bioctal) and human error, some of the values
   specified as outputs for the detection subsystem are in hexadecimal,
   not the bioctal the engineer developing that subsystem expects --
   including, in the case of one type of lizard, "4b 4f".  The result is
   that the detector displays "NL" (No Lizards) when it should display
   "KO" (Komodo dragon).  This may be considered prejudicial to the
   security of the user of the device.

   Extensive research has uncovered no other security-related scenarios
   to date.

5.  IANA Considerations

   This document has no IANA actions.

6.  Conclusion

   Bioctal is a significant advance over hexadecimal technology and
   promises to reduce the small (but assuredly non-zero) contribution to
   anthropogenic global warming of mental hex-to-binary conversions.
   Since the mnemonic basis of the alphabet is independent of English or
   any other particular natural language, there is no reason that it
   should not be adopted immediately around the world, excepting perhaps
   certain islands of Indonesia to which _Varanus komodoensis_ is
   native.

7.  Informative References

   [Martin]   Martin, B. A., "Letters to the editor: On binary
              notation", Communications of the ACM, Vol. 11, No. 10,
              DOI 10.1145/364096.364107, October 1968,
              <https://doi.org/10.1145/364096.364107>.

   [Miller]   Miller, G. A., "The Magical Number Seven, Plus or Minus
              Two: Some Limits on Our Capacity for Processing
              Information", Psychological Review, Vol. 101, No. 2, 1956.

   [UNIVAC]   Sperry Rand Corporation, "Programmers Reference Manual for
              UNIVAC 1218 Computer", Revision C, Update 2, November
              1969, <http:/bitsavers.computerhistory.org/pdf/univac/
              military/1218/PX2910_Univac1218PgmrRef_Nov69.pdf>.

   [USASCII]  American National Standards Institute, "Coded Character
              Set -- 7-bit American Standard Code for Information
              Interchange", ANSI X3.4, 1986.

Acknowledgments

   The author is indebted to R. Goldberg for assistance with Section 4.

Author's Address

   Michael Breen
   mbreen.com
   Email: rfc@mbreen.com