Part of the Mathematics glossary:

Binary describes a numbering scheme in which there are only two possible values for each digit: 0 and 1. The term also refers to any digital encoding/decoding system in which there are exactly two possible states.In digital data memory, storage, processing, and communications, the 0 and 1 values are sometimes called "low" and "high," respectively.

Binary numbers look strange when they are written out directly.This is because the digits' weight increases by powers of 2, rather than by powers of 10.In a digital numeral, the digit furthest to the right is the "ones" digit; the next digit to the left is the "twos" digit; next comes the "fours" digit, then the "eights" digit, then the "16s" digit, then the "32s" digit, and so on.The decimal equivalent of a binary number can be found by summing all the digits.For example, the binary 10101 is equivalent to the decimal 1 + 4 + 16 = 21:

DECIMAL = 21 64 32 16 8 4 2 1
BINARY = 10101 0 0 1 0 1 0 1

The numbers from decimal 0 through 15 in decimal, binary, octal, and hexadecimal form are listed below.

DECIMAL BINARY OCTAL HEXA-
DECIMAL
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

This was last updated in June 2007
Posted by: Margaret Rouse

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