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 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^1} ), and no sets of ones (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^0} ). In binary numbering, system each digit position represents a power of two. The same number, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10} represents the value consisting of one set of twos ($2^{1}$) and no sets of ones (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2^0} ) which is represented by the number 2 in the decimal system.

Decimal	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 100_{10} = (1 \times 10^2) + (0 \times 10^1) + (0 \times 10^0)}
Binary	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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)