![]() UCS-2 characters, code units in the UTF-16 character encoding Unsigned: From 0 to 255, which equals 2 8 − 1 Signed: From −128 to 127, from −(2 7) to 2 7 − 1ĪSCII characters, code units in the UTF-8 character encoding Unsigned: From 0 to 15, which equals 2 4 − 1 Signed: From −8 to 7, from −(2 3) to 2 3 − 1īinary-coded decimal, single decimal digit representation Range (assuming two's complement for signed) 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). Many modern CPUs provide limited support for decimal integers as an extended datatype, providing instructions for converting such values to and from binary values. These values generally require data sizes of 4 bits per decimal digit (sometimes called a nibble), usually with additional bits for a sign. Some older computer architectures used decimal representations of integers, stored in binary-coded decimal (BCD) or other format. An integer in one programming language may be a different size in a different language or on a different processor. ![]() Not all language implementations define variables of all integer sizes, and defined sizes may not even be distinct in a particular implementation. Some computer languages define integer sizes in a machine-independent way others have varying definitions depending on the underlying processor word size. Other possibilities include offset binary, sign-magnitude, and ones' complement. 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. 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. There are four well-known ways to represent signed numbers in a binary computing system. ![]() ![]() 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. An integral type with n bits can encode 2 n numbers for example an unsigned type typically represents the non-negative values 0 through 2 n−1. The width or precision of an integral type is the number of bits in its representation. The order of the memory bytes storing the bits varies see endianness. The most common representation of a positive integer is a string of bits, using the binary numeral system. Unlike mathematical integers, a typical datum in a computer has some minimal and maximum possible value. The internal representation of this datum is the way the value is stored in the computer's memory. Some programming languages also permit digit group separators. Some programming languages allow other notations, such as hexadecimal (base 16) or octal (base 8). Īn integer value is typically specified in the source code of a program as a sequence of digits optionally prefixed with + or −. Integral types may be unsigned (capable of representing only non-negative integers) or signed (capable of representing negative integers as well). The value of an item with an integral type is the mathematical integer that it corresponds to. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer. The size of the grouping varies so the set of integer sizes available varies between different types of computers. Integers are commonly represented in a computer as a group of binary digits (bits). Integral data types may be of different sizes and may or may not be allowed to contain negative values. In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers.
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