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Datum of integral data type
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer.

The value of an item with an integral type is the mathematical integer that it corresponds to. Integral types may be unsigned (capable of representing only non negative integers) or signed (capable of representing negative integers as well). An integer value is typically specified in the source code of a program as a sequence of digits optionally prefixed with + or −. Some programming languages allow other notations, such as hexadecimal (base 16) or octal (base 8). Some programming languages also permit digit group separators. The internal representation of this datum is the way the value is stored in the computer's memory. Unlike mathematical integers, a typical datum in a computer has some minimal and maximum possible value. The most common representation of a positive integer is a string of bits, using the binary numeral system. The order of the memory bytes storing the bits varies; see endianness. The width, precision, or bitness of an integral type is the number of bits in its representation. An integral type with n bits can encode 2n numbers; for example an unsigned type typically represents the non negative values 0 through 2n−1. Other encodings of integer values to bit patterns are sometimes used, for example binary coded decimal or Gray code, or as printed character codes such as ASCII. There are four well known ways to represent signed numbers in a binary computing system. The most common is two's complement, which allows a signed integral type with n bits to represent numbers from −2(n−1) through 2(n−1)−1. Two's complement arithmetic is convenient because there is a perfect one to one correspondence between representations and values (in particular, no separate +0 and −0), and because addition, subtraction and multiplication do not need to distinguish between signed and unsigned types. Other possibilities include offset binary, sign magnitude, and ones' complement. Some computer languages define integer sizes in a machine independent way; others have varying definitions depending on the underlying processor word size. Not all language implementations define variables of all integer sizes, and defined sizes may not even be distinct in a particular implementation. An integer in one programming language may be a different size in a different language, on a different processor, or in an execution context of different bitness; see
Some older computer architectures used decimal representations of integers, stored in binary coded decimal (BCD) or other format. These values generally require data sizes of 4 bits per decimal digit (sometimes called a nibble), usually with additional bits for a sign. Many modern CPUs provide limited support for decimal integers as an extended datatype, providing instructions for converting such values to and from binary values. Depending on the architecture, decimal integers may have fixed sizes (e. g., 7 decimal digits plus a sign fit into a 32 bit word), or may be variable length (up to some maximum digit size), typically occupying two digits per byte (octet).

The term byte initially meant 'the smallest addressable unit of memory'. In the past, 5 , 6 , 7 , 8 , and 9 bit bytes have all been used. There have also been computers that could address individual bits ('bit addressed machine'), or that could only address 16 or 32 bit quantities ('word addressed machine'). The term byte was usually not used at all in connection with bit and word addressed machines. The term octet always refers to an 8 bit quantity. It is mostly used in the field of computer networking, where computers with different byte widths might have to communicate. In modern usage byte almost invariably means eight bits, since all other sizes have fallen into disuse; thus byte has come to be synonymous with octet.

The term 'word' is used for a small group of bits that are handled simultaneously by processors of a particular architecture. The size of a word is thus CPU specific. Many different word sizes have been used, including 6 , 8 , 12 , 16 , 18 , 24 , 32 , 36 , 39 , 40 , 48 , 60 , and 64 bit. Since it is architectural, the size of a word is usually set by the first CPU in a family, rather than the characteristics of a later compatible CPU. The meanings of terms derived from word, such as longword, doubleword, quadword, and halfword, also vary with the CPU and OS.

The standard integer size is platform dependent. In C, it is denoted by and required to be at least 16 bits. Windows and Unix systems have 32 bit s on both 32 bit and 64 bit architectures.

In the C99 version of the C programming language and the C++11 version of C++, a long long type is supported that has double the minimum capacity of the standard long. This type is not supported by compilers that require C code to be compliant with the previous C++ standard, C++03, because the type did not exist in C++03. For an ANSI/ISO compliant compiler, the minimum requirements for the specified ranges, that is, −(263−1) This can be an issue when exchanging code and data between platforms, or doing direct hardware access. Thus, there are several sets of headers providing platform independent exact width types. The C standard library provides stdint. h; this was introduced in C99 and C++11.