Integer (computer science)

In computer science, the term integer is used to refer to any data type which can represent some subset of the mathematical integers. These are also known as integral data types.
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Value and representation
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 integral type with n bits can encode 2^{n} numbers; for example an unsigned type typically represents the nonnegative values 0 through 2^{n}−1.
There are three different ways to represent negative numbers in a binary numeral 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 onetoone correspondence between representations and values, and because addition and subtraction do not need to distinguish between signed and unsigned types. The other possibilities are signmagnitude and ones' complement.
Another, rather different, representation for integers is binarycoded decimal, which is still commonly used in mainframe financial applications and in databases.
Common integral data types
bits  name  range  uses 

8  byte, octet  Signed: −128 to +127 Unsigned: 0 to +255  ASCII characters, C char (minimum), Java byte 
16  halfword, word  Signed: −32,768 to +32,767 Unsigned: 0 to +65,535  UCS2 characters, C short int (minimum), C int (minimum), Java char, Java short 
32  word, doubleword, longword  Signed: −2,147,483,648 to +2,147,483,647 Unsigned: 0 to +4,294,967,295  UCS4 characters, True color with alpha, C int (usual), C long int (minimum), Java int 
64  doubleword, longword, quadword  Signed: −9,223,372,036,854,775,808 to +9,223,372,036,854,775,807 Unsigned: 0 to +18,446,744,073,709,551,615  C long int (on 64bit machines), C99 long long int (minimum), Java long 
128  Signed: −170,141,183,460,469,231,731,687,303,715,884,105,728 to +170,141,183,460,469,231,731,687,303,715,884,105,727 Unsigned: 0 to +340,282,366,920,938,463,463,374,607,431,768,211,455  C int __attribute__ ((mode(TI))) (on 64bit machines using gcc)  
n  nbit integer  Signed: <math>2^{n1}<math> to <math>2^{n1} 1<math>
Unsigned: 0 to <math>2^{n}1<math> 
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 hardwaresupported type. Many languages also have bitfield types (a specified number of bits, usually constrained to be less than the maximum hardwaresupported width) and range types (which can represent only the integers in a specified range).
Some languages, such as Lisp, REXX and Haskell, support arbitrary precision integers (also known as infinite precision integers or bignums). Other languages which do not support this concept as a toplevel construct may have libraries available to represent very large numbers using arrays of smaller variables, such as Java's BigInteger class. These use as much of the computer’s memory as is necessary to store the numbers; however, a computer has only a finite amount of storage, so they too can only represent a finite subset of the mathematical integers. These schemes support very large numbers, for example one kilobyte of memory could be used to store numbers up to about 2466 digits long.
A Boolean or Flag type is a type which can represent only two values: 0 and 1, usually 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 of addressing and speed of access.
A fourbit quantity is known as a nibble (when eating, being smaller than a bite) or nybble (being a pun on the form of the word byte). One nibble corresponds to one digit in hexadecimal and holds one digit or a sign code in binarycoded decimal.
Pointers
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.
Bytes and octets
 Main article: Byte
The term byte initially meant ‘the least addressable unit of memory’. In the past, 5, 6, 7, 8, and 9bit bytes have all been used. There have also been computers that could address individual bits (‘bitaddressed machine’), or that could only address 16 or 32bit quantities (‘wordaddressed machine’). The term byte was usually not used at all in connection with bit and wordaddressed machines.
The term octet always refers to an 8bit 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; byte has thus come to be synonymous with octet.
Bytes are used as the unit of computer storage of all kinds. One might speak of a 50byte text string, a 100 KB (kilobyte) file, a 128 MB (megabyte) RAM module, or a 30 GB (gigabyte) hard disk. The prefixes used for byte measurements are written the same as SI prefixes used for other measurements, but they often have somewhat different values (see binary prefix for further discussion).
In particular, hard disk manufacturers describe their products using the SI units, making their disks sound larger than one might expect. As drives become larger, the difference is growing (see table below).
Prefix  Name  SI Meaning  Binary meaning  Size difference 

k or K  kilo  10^{3} = 1000  2^{10} = 1024  2.40% 
M  mega  10^{6} = 1000^{2}  2^{20} = 1024^{2}  4.86% 
G  giga  10^{9} = 1000^{3}  2^{30} = 1024^{3}  7.37% 
T  tera  10^{12} = 1000^{4}  2^{40} = 1024^{4}  9.95% 
P  peta  10^{15} = 1000^{5}  2^{50} = 1024^{5}  12.59% 
Words
 Main article: Word (computer science)
The term word is used for a small group of bits which are handled simultaneously by processors of a particular architecture. The size of a word is thus CPUspecific. Many different word sizes have been used, including 6, 8, 12, 16, 18, 24, 32, 36, 39, 48, 60, and 64bit. 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.
As of 2004, 32bit word sizes are most common among generalpurpose computers, with 64bit machines used mostly for large installations. ‘Embedded’ processors with 8 and 16bit word size are still common. The 36bit word length was common in the early days of computers, but word sizes that aren’t a multiple of 8 have vanished along with non8bit bytes.de:Integer (Datentyp) pl:Liczby całkowite (zapis komputerowy) ru:Целый тип