binary system

binary system numeration system based on powers of 2, in contrast to the familiar decimal system , 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 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 In mathematics, number system having a base of 2 (the decimal system has a base of 10). It is most appropriate to computers since it is simple and corresponds to the open (0), and closed (1) states of switch, or logic gate, on which computers are based.

binary system Usually, the binary number system, i.e. the positional number system with base 2. This is the number system most commonly used in computers. A binary digit (or bit) is either 0 or 1. The representation of numbers by binary digits is called binary notation.

The term binary system is also used to describe any system in which there are just two possible states. For example, each of the elements comprising the memory of any computer is a binary system, one of whose states is used to denote the binary digit 0 and the other to denote the binary digit 1. It is customary to refer to such a storage element, or to the unit of information in any binary system, as a bit.