(mathematics) | **hexadecimal** - (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
-----
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. | |