Computer number format

A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. Numerical values are stored as groupings of bits, such as bytes and words. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the encoding used by the computer's instruction set generally requires conversion for external use, such as for printing and display. Different types of processors may have different internal representations of numerical values and different conventions are used for integer and real numbers. Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory. Integer (computer science) Computers represent data in sets of binary digits. The representation is composed of bits, which in turn are grouped into larger sets such as bytes. A bit is a binary digit that represents one of two states. The concept of a bit can be understood as a value of either 1 or 0, on or off, yes or no, true or false, or encoded by a switch or toggle of some kind. While a single bit, on its own, is able to represent only two values, a string of bits may be used to represent larger values. For example, a string of three bits can represent up to eight distinct values as illustrated in Table 1. As the number of bits composing a string increases, the number of possible 0 and 1 combinations increases exponentially. A single bit allows only two value-combinations, two bits combined can make four separate values, three bits for eight, and so on, increasing with the formula 2n. The amount of possible combinations doubles with each binary digit added as illustrated in Table 2. Groupings with a specific number of bits are used to represent varying things and have specific names. A byte is a bit string containing the number of bits needed to represent a character.