Re: Hexadecimal digits

From: Otto Stolz (
Date: Sat Jun 05 2010 - 09:33:03 CDT

  • Next message: Michael Everson: "Re: Hexadecimal digits"

    Am 2010-06-05 00:04, schrieb Luke-Jr:
    > Base 16 is superior in many various ways, the most obvious being easier
    > division (both visibly and numeric).

    This is a red herring, IMHO.

    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.

    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.

    Of course, a larger base needs less digits (on average)
    for any given number; hence divisions for large numbers
    tend to take less steps in the hexadekadic system than
    in the decimal one; whether this will outweigh the larger
    multiplication table to be used, is, I reckon, a matter
    of taste. Somewhere, there must be an optimum: I cannot
    imagine people to learn, and memorize, e. g., the 3600
    entries of the multiplication table for base 60.

    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.

    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.

    Best wishes,
       Otto Stolz

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