**From:** Otto Stolz (*Otto.Stolz@uni-konstanz.de*)

**Date:** Sat Jun 05 2010 - 09:33:03 CDT

**Previous message:**William_J_G Overington: "Re: Overloading Unicode"**In reply to:**Luke-Jr: "Re: Hexadecimal digits"**Next in thread:**Michael Everson: "Re: Hexadecimal digits"**Reply:**Michael Everson: "Re: Hexadecimal digits"**Reply:**Luke-Jr: "Re: Hexadecimal digits"**Reply:**Hans Aberg: "Re: Hexadecimal digits"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Am 2010-06-05 00:04, schrieb Luke-Jr:

*> Base 16 is superior in many various ways, the most obvious being easier
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*> division (both visibly and numeric).
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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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