RE: Hexadecimal digits

From: CE Whitehead (
Date: Mon Jun 07 2010 - 21:36:48 CDT

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    Hi, I've gotten a bit behind on this discussion; oh well.

    It really does seem to be getting circular (and getting away from the concerns of encoding) unless Luke comes back with a list of facebook users, his private use encoding system, etc. and shows that his system is in use.


    From: Luke-Jr (
    Date: Sat Jun 05 2010 - 10:29:03 CDT

    On Saturday 05 June 2010 09:33:03 am Otto Stolz wrote:
    >> In the decimal systems, you can easier divide by 2, 5,
    >> and powers of 10, whilst in the hexadekadic system,
    >> you can easier divide by many powers of two, and all
    >> powers of 16.

    > And 4, and 8. Many repeating fractions also become more accurate with base 16.

    >> For arbitrary divisors, the decimal system seems to be
    >> easier, as you would use the same division algorithm,
    >> in both systems, however with different tables (dubbed
    >> “multiplication table” or, less formally, “times table”)
    >> that comprise 100 vs. 256 entries. Hence, the the hexa-
    >> dekadic multiplication table should be 2½ times as hard
    >> to learn, and memorize, as the decimal one.

    > Does anyone seriously memorise multiplication tables...?
    Doing so can speed up test taking for persons who have to pass entrance examinations -- not to mention
    of course rapid calculations about payments, interest, and more.
    (Indeed memorizing tables through 12 by 12 albeit in base 10 was a requirement for promotion to third grade
    in my day in school but things have changed I suppose -- for one thing candidates are allowed to take calculators to the S.A.T. now)

    >> This whole deliberation is, of course, purely academic.
    >> In real life, you will have to use the decimal system
    >> as everybody else does, lest you wont be misunderstood.

    > Only when/if you deal with "everybody else".
    > And then you need only convert, not use it for your calculations.
    You need the decimal system for most college entrance exams, prices in the real world (till we change the dollar, get another monetary system -- maybe we need to -- but we are not the only country on a system of one's, one-hundreds, etc; there is the Mexican peso and more -- but the Mexican peso comes from the base 8/16 pieces of eight -- maybe they had computers way back then and we just do not know -- that info got somehow lost; the British however always did their own thing; I'm not a Brit I guess), taxes, etc.

    You need the hexadecimal system to 'talk to computers in assembly language' (but need to talk in straight base 2 if you are writing machine code -- otherwise you need a compiler).

    You can also use hexa whatever (don't want to say the 'decimal' part here) in books describing assembly language -- books for people even. (Why not? Although it does after all take a human to write the code that makes a computer 'really foul things up;' my dad who has written some code himself always told me that base 16 and base 8 were invented to make it easier for PEOPLE to write code for computers -- thus people would not have to write in 1s and 0s.)

    IMO an encoding system for hexadecimals -- inspired by an extant private use set of encodings, having a definable/identifiable community of users with examples of usage online or something -- should fly as a proposal.


    There is no real perfect base system but base 6 or 12 or some multiple thereof would facilitate conversion between base 2 and base 3 tertiary but the circuits are going to be complicated.
    But base 6 or 12 would make counting on the fingers more difficult.
    (But as you've said above people don't memorize tables or use fingers; they all have calculators and computers.)
    But we've strayed from unicode concerns in this discussion, I think.

    (As for isolation, go ahead yourself, but will your children ever mix? If so will they need to understand base 10?)

    >> You may wonder, why I am using the term “hexadekadic”.
    >> This is because, “hexadeka” is the Greek word for 16,
    >> whilst the Latin word ist “sedecim”; there is no language
    >> known that has “hexadecim”, or anything alike, for 16.

    > I prefer "tonal", since "hexadecimal"/"hexadekadic" both imply a decimal base.

    6 and 10. I don't know whether the base is meant to be six or ten . . .

    > . . .
    From: Luke-Jr (
    Date: Sat Jun 05 2010 - 12:35:36 CDT
    > I've also created a "Hexadecimal / Tonal Mathematics" group on Facebook, to
    > promote using it in daily life. ;)
    Who else goes to your facebook page? How many friends?
    And what system of encoding have you all agreed on for encoding characters?
    You might develop your case thus; otherwise I fear that any discussion will be 'circular' and pointless.



    C. E. Whitehead

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