# binary system

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Related to binary system: decimal system, Binary star system

## binary system,

numeration**numeration,**

in mathematics, process of designating numbers according to any particular system; the number designations are in turn called numerals. In any place value system of numeration, a base number must be specified, and groupings are then made by powers of the base number.

**.....**Click the link for more information. system based on powers of 2, in contrast to the familiar decimal system

**decimal system**

[Lat.,=of tenths], numeration system based on powers of 10. A number is written as a row of digits, with each position in the row corresponding to a certain power of 10.

**.....**Click the link for more information. , which is based on powers of 10. In the binary system, only the digits 0 and 1 are used. Thus, the first ten numbers in binary notation, corresponding to the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in decimal notation, are 0, 1, 10, 11, 100, 101, 110, 111, 1000, and 1001. Since each position indicates a specific power of 2, just as the number 342 means (3 × 10

^{2}) + (4 × 10

^{1}) + (2 × 10

^{0}), the decimal equivalent of a binary number can be calculated by adding together each digit multiplied by its power of 2; for example, the binary number 1011010 corresponds to (1 × 2

^{6}) + (0 × 2

^{5}) + (1 × 2

^{4}) + (1 × 2

^{3}) + (0 × 2

^{2}) + (1 × 2

^{1}) + (0 × 2

^{0}) = 64 + 0 + 16 + 8 + 0 + 2 + 0 = 90 in the decimal system. Binary numbers are sometimes written with a subscript "b" to distinguish them from decimal numbers having the same digits. As with the decimal system, fractions can be represented by digits to the right of the binary point (analogous to the decimal point). A binary number is generally much longer than the decimal equivalent; e.g., the number above, 1011010

_{b}, contains seven digits while its decimal counterpart, 90, contains only two. This is a disadvantage for most ordinary applications but is offset by the greater simplicity of the binary system in computer

**computer,**

device capable of performing a series of arithmetic or logical operations. A computer is distinguished from a calculating machine, such as an electronic calculator, by being able to store a computer program (so that it can repeat its operations and make logical

**.....**Click the link for more information. applications. Since only two digits are used, any binary digit, or bit, can be transmitted and recorded electronically simply by the presence or absence of an electrical pulse or current. The great speed of such devices more than compensates for the fact that a given number may contain a large number of digits.

## binary system

[′bīn·ə·rē ′sis·təm] (astronomy)

(engineering)

Any system containing two principal components.

(mathematics)

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