Integer (computer science)
- This article should be merged with computer numbering formats.
| Table of contents |
|
2 Common integral data types 3 Pointers 4 Bytes and Octets 5 Words |
The value of a datum with an integral type is the mathematical
integer that it corresponds to. The representation of this datum
is the way the value is stored in the computer's memory. Integral
types may be unsigned (capable of representing only nonnegative
integers) or signed (capable of representing negative integers as
well).
The most common representation of a positive integer is a string of
bits, using the binary numeral system. The order of the bits
varies; see Endianness. The width or precision of an
integral type is the number of bits in its representation. An
unsigned integral type with n bits can represent numbers from 0 to
.
There are three different ways to represent negative numbers in a binary numeral system. The
most common is twos complement, which allows a signed integral
type with n bits to represent numbers from
to . Twos complement arithmetic is convenient
because there is a perfect one-to-one correspondence
between representations and values, and because addition and
subtraction do not need to distinguish between signed and unsigned
types. The other possibilities are sign and magnitude and
ones complement.
Another, rather different representation for integers is
binary-coded decimal, which was once commonly used (notably in financial applications)
but is now rare.
Value and Representation
Common integral data types
| bits | name | uses |
|---|---|---|
| 8 | byte, octet | ASCII characters, C char (minimum), Java byte |
| 16 | word | UCS-2 characters, C short int (minimum), C int (minimum), Java char, Java short int |
| 32 | word, doubleword, longword | UCS-4 characters, C int (usual), C long int (minimum), Java int |
| 64 | longword, quadword | C long int (on 64-bit machines), C99 long long int (minimum), Java long int |
Different CPUs support different integral data types. Typically, hardware will support both signed and unsigned types but only a small, fixed set of widths.
The table above lists integral type widths that are supported in hardware by common processors. High level programming languages provide more possibilities. It is common to have a "double width" integral type that has twice as many bits as the biggest hardware-supported type. Many languages also have bit-field types (a specified number of bits, usually constrained to be less than the maximum hardware-supported width) and range types (can represent only the integers in a specified range).
Some languages, such as Lisp, support "infinite precision" integers, also known as arbitrary precision integers or bignums. These are limited only by the size of the computer's memory, so they can represent very large (but not truly infinite) integers.
A Boolean type is a special range type that can represent only two values: 0 and 1, identified with false and true respectively. This type can be stored in memory using a single bit, but is often given a full byte for convenience.
A four-bit quantity is known as a nybble; this is a joke on the
word "byte". One nybble corresponds to one digit in hexadecimal
and binary-coded decimal.
A pointer is often, but not always,
represented by an integer of specified width. This is often, but not
always, the widest integer that the hardware supports directly. The
value of this integer is the memory address of whatever the
pointer points to.
The term byte initially meant "the least 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 not
used at all in connection with these 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" invariably means eight bits, since all other
sizes have fallen into disuse; "octet" has thus come to be synonymous
with "byte".
Bytes are used as the unit of computer memory of
all kinds. One speaks of a 50 byte text string, a 100 kB (kilobyte)
file, a 128 MB (megabyte) RAM module, a 30 GB (gigabyte) hard disk.
The prefixes used for byte measurements are similar to the
SI prefixes used for other measurements, but they do not have the
same meanings. (See SI prefix for further discussion.)
Pointers
Bytes and Octets
| prefix | Usual meaning | Meaning when applied to bytes |
|---|---|---|
| k | 103 = 1000 | 210 = 1024 |
| M | 106 = 10002 | 220 = 10242 |
| G | 109 = 10003 | 230 = 10243 |
| T | 1012 = 10004 | 240 = 10244 |
| P | 1015 = 10005 | 250 = 10245 |
Unscrupulous hard disk manufacturers describe their products using
the power-of-1000 meanings, which is the subject of a current
(2003) false advertising lawsuit.
The term word initially meant "the size of an address in the system
memory", and was thus CPU- and OS-specific. One
could say that the IBM 370 had 32-bit words, and the 8086 had
16-bit words. 8-, 12-, 16-, 32-, 36-, 60- and 64-bit words have all
been used. The meanings of terms derived from "word", such as "long
word", "double word", and "half word", also vary with the CPU and OS.
More recently, the popularity of 16- and 32-bit operating systems
based on the x86 architecture has caused a substantial population
of speakers to take "word" to always refer to a 16-bit quantity.
It is wise to avoid these terms entirely, due to the potential for
confusion.Words
