Hexadecimal Numbers

Computers do not understand every-day (decimal=base₁₀) numbers, but work with binary numbers (numbers that only use the digits 0 and 1=base₂).

This can make for some very long-winded numbers. See the examples in the table below. In the early days of computers, engineers started to group binary digits in threes to read them (octal numbers=base₈). When personal computers came along in the late seventies, the number of binary digits (bits) in a standard unit of memory (Byte) was eight. In octal numbers this became a two-bit digit followed by two three-bit digits.

It seemed more logical to split these eight-bit digits into two four-bit digits. Thus a Byte becomes two four-bit (hexadecimal=base₁₆) numbers. Having only ten digits in decimal numbers, the shortfall is made up by adopting the letters 'a' to 'f' for the missing digits.

Whatever the base, arithmetic is the same. Try some for yourself.

Numbers in different systems
Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
2	10	2	2
3	11	3	3
4	100	4	4
5	101	5	5
6	110	6	6
7	111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	a
11	1011	13	b
12	1100	14	c
13	1101	15	d
14	1110	16	e
15	1111	17	f
16	10000	20	10
17	10001	21	11
18	10010	22	12
19	10011	23	13
20	10100	24	14
21	10101	25	15
22	10110	26	16
23	10111	27	17
24	11000	30	18
25	11001	31	19
30	11110	36	1e
35	100011	43	23
40	101000	50	28
45	101101	55	2d
50	110010	62	32
55	110111	67	37
60	111100	74	3c
100	1100100	144	64

This lesson is available 18₁₆/111₂ ;-)