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hexadecimal

mathematics (Or "hex") Base 16. A number representation

using the digits 0-9, with their usual meaning, plus the

letters A-F (or a-f) to represent hexadecimal digits with

values of (decimal) 10 to 15. The right-most digit counts

ones, the next counts multiples of 16, then 16^2 = 256, etc.

For example, hexadecimal BEAD is decimal 48813:

digit weight value

B = 11 16^3 = 4096 11*4096 = 45056

E = 14 16^2 = 256 14* 256 = 3584

A = 10 16^1 = 16 10* 16 = 160

D = 13 16^0 = 1 13* 1 = 13

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BEAD = 48813

There are many conventions for distinguishing hexadecimal

numbers from decimal or other bases in programs. In C for

example, the prefix "0x" is used, e.g. 0x694A11.

Hexadecimal is more succinct than binary for representing

bit-masks, machines addresses, and other low-level constants

but it is still reasonably easy to split a hex number into

different bit positions, e.g. the top 16 bits of a 32-bit word

are the first four hex digits.

The term was coined in the early 1960s to replace earlier

"sexadecimal", which was too racy and amusing for stuffy

IBM, and later adopted by the rest of the industry.

Actually, neither term is etymologically pure. If we take

"binary" to be paradigmatic, the most etymologically correct

term for base ten, for example, is "denary", which comes from

"deni" (ten at a time, ten each), a Latin "distributive"

number; the corresponding term for base sixteen would be

something like "sendenary". "Decimal" is from an ordinal

number; the corresponding prefix for six would imply something

like "sextidecimal". The "sexa-" prefix is Latin but

incorrect in this context, and "hexa-" is Greek. The word

octal is similarly incorrect; a correct form would be

"octaval" (to go with decimal), or "octonary" (to go with

binary). If anyone ever implements a base three computer,

computer scientists will be faced with the unprecedented

dilemma of a choice between two *correct* forms; both

"ternary" and "trinary" have a claim to this throne.