October 27, 2021

Hexadecimal Number System


A base 16 (radix 16) number system, i.e. increasing powers of 16. Introduced by IBM - legend has it that the company refused to countenance the more accurate sexadecimal name.

Besides the numbers 0 ..9, hex uses the letters A, B, C, D, E, and F to represent the decimal equivalents 10, 11, 12, 13, 14 and 15 (see rules).
For example, decimal value 31 has hex value 1F

163=4096 162=256 161=16 160=1
0 0 1 F

1F = 1 lot of 16 plus F lots of 1

A hex digit represents 4 binary digits (0000 to 1111) and two hex digits can represent one byte. This simple segmenting of binary into hex is an improvement on octal representation as a means of viewing binary data in modern machines. However, it is worth bearing in mind that if computers still employed a 6-digit byte, rather than the ubiquitous 8-bit byte, then the octal system, where an octal digit is equivalent to 3-bits, would be better for segmenting and viewing binary numbers.
See the DEC PDP-10 which used a 36-bit word size. http://www.encyclopedia4u.com/p/pdp-10.html

Example Usage

Hex has many applications, of which the following are just a few:


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