Integer (computer science): Difference between revisions

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.

Value and representation

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 § Words.

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).

Syntax

Literals for integers can be written as regular Arabic numerals, consisting of a sequence of digits and with negation indicated by a minus sign before the value. However, most programming languages disallow use of commas or spaces for digit grouping. Examples of integer literals are:

• 42
• 10000
• -233000

There are several alternate methods for writing integer literals in many programming languages:

• Many programming languages, especially those influenced by C, prefix an integer literal with 0X or 0x to represent a hexadecimal value, e.g. 0xDEADBEEF. Other languages may use a different notation, e.g. some assembly languages append an H or h to the end of a hexadecimal value.
• Perl, Ruby, Java, Julia, D, Go, Rust and Python (starting from version 3.6) allow embedded underscores for clarity, e.g. 10_000_000, and fixed-form Fortran ignores embedded spaces in integer literals. C (starting from C23) and C++ use single quotes for this purpose.
• In C and C++, a leading zero indicates an octal value, e.g. 0755. This was primarily intended to be used with Unix modes; however, it has been criticized because normal integers may also lead with zero. As such, Python, Ruby, Haskell, and OCaml prefix octal values with 0O or 0o, following the layout used by hexadecimal values.
• Several languages, including Java, C#, Scala, Python, Ruby, OCaml, C (starting from C23) and C++ can represent binary values by prefixing a number with 0B or 0b.

See also

• Arbitrary-precision arithmetic
• Binary-coded decimal (BCD)
• C data types
• Integer overflow
• Signed number representations