Binary numeral system

The binary numbering system (also referred to as base-2, or radix-2), represents numbers using only the digits 0 and 1. This is in contrast with the more familiar decimal system (a.k.a. base-10, radix-10) which uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In the decimal system, each digit position represents a power of ten. The number $10$ represents the value consisting of one set of tens ($10^{1}$), and no sets of ones ($10^{0}$). In binary numbering, system each digit position represents a power of two. The same number, $10$ represents the value consisting of one set of twos ($2^{1}$) and no sets of ones ($2^{0}$) which is represented by the number 2 in the decimal system.

Decimal	$100_{10}=(1\times 10^{2})+(0\times 10^{1})+(0\times 10^{0})$
Binary	$100_{2}=(1\times 2^{2})+(0\times 2^{1})+(0\times 2^{0})=4_{10}+0+0=4_{10}$

Because the number of digits in the binary representation of a value can grow quickly, binary values are often represented in the hexadecimal numbering system (base-16), which uses the digits 0 through 9, followed by the letters A through F to represent the values ten, eleven, twelve, thirteen, fourteen, and fifteen.

Decimal	Binary	Hexadecimal
0	0	0
1	1	1
2	10	2
3	11	3
4	100	4
5	101	5
6	110	6
7	111	7
8	1000	8
9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F
16	10000	10

--Kevin J. Cole 10:24, 5 March 2007 (CST)