September 21, 2020
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
16^{3}=4096 | 16^{2}=256 | 16^{1}=16 | 16^{0}=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:
- RGB colour representation http://www.lynda.com/hexh.html
- NIC (Network Interface Card) MAC (Media Access Control) addresses http://www.cityu.edu.hk/csc/deptweb/facilities/ctnet/wlan/machelp.htm
- Extended ASCII Chart used for representing 28 or 256 characters (0 ..255), including all of those on your keyboard plus a few esoteric symbols. Any ASCII value can be represented by a 2 digit hex i.e. 00 .. FF. http://www.asciitable.com/
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