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cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia redirected from signed integer 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 1 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 edit 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 2 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 3 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 4 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 non negative values 0 through 2 n 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 common integral data types edit bits name range assuming two s complement for signed decimal digits uses implementations c c c pascal and delphi java sql a fortran d rust 4 nibble semioctet signed from 8 to 7 from 2 3 to 2 3 1 0 9 binary coded decimal single decimal digit repre sen ta tion unsigned from 0 to 15 which equals 2 4 1 1 2 8 byte octet i8 u8 signed from 128 to 127 from 2 7 to 2 7 1 2 11 ascii characters code units in the utf 8 character encoding int8_t signed char b sbyte system sbyte shortint byte java lang byte tinyint integer c byte i8 unsigned from 0 to 255 which equals 2 8 1 2 41 uint8_t unsigned char b byte system byte byte n a unsigned tinyint n a ubyte u8 16 halfword word short i16 u16 signed from 32 768 to 32 767 from 2 15 to 2 15 1 4 52 ucs 2 characters code units in the utf 16 character encoding int16_t short b int b short system int16 smallint short java lang short smallint integer c short i16 unsigned from 0 to 65 535 which equals 2 16 1 4 82 uint16_t unsigned b unsigned int b ushort system uint16 word char d java lang character unsigned smallint n a ushort u16 32 word long doubleword longword int i32 u32 signed from 2 147 483 648 to 2 147 483 647 from 2 31 to 2 31 1 9 33 utf 32 characters true color with alpha fourcc pointers in 32 bit computing int32_t int b long b int system int32 longint integer e int java lang integer int integer c int i32 unsigned from 0 to 4 294 967 295 which equals 2 32 1 9 63 uint32_t unsigned b unsigned int b unsigned long b uint system uint32 longword dword cardinal e n a unsigned int n a uint u32 64 word doubleword longword long long long quad quadword qword int64 i64 u64 signed from 2 63 to 2 63 1 18 96 time e g milli seconds since the unix epoch pointers in 64 bit computing int64_t long b long long b long system int64 int64 long java lang long bigint integer c long i64 unsigned from 0 to 2 64 1 19 27 uint64_t unsigned long long b ulong system uint64 uint64 qword n a unsigned bigint n a ulong u64 128 octaword double quadword i128 u128 signed from 2 127 to 2 127 1 38 23 complex scientific cal cula tions ipv6 addresses guids only available as non standard or compiler specific extensions cent f i128 unsigned from 0 to 2 128 1 38 53 ucent f u128 n n bit integer general case signed 2 n 1 to 2 n 1 1 n 1 log 10 2 c23 _bitint n signed _bitint n ada range 2 n 1 2 n 1 1 unsigned 0 to 2 n 1 n log 10 2 c23 unsigned _bitint n ada range 0 2 n 1 mod 2 n standard libraries or third party arbitrary arithmetic libraries bigdecimal or decimal classes in many languages such as python c etc 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 that can represent only the integers in a specified range some languages such as lisp smalltalk rexx haskell python and raku support arbitrary precision integers also known as infinite precision integers or bignums other languages that do not support this concept as a top level construct may have libraries available to represent very large numbers using arrays of smaller variables such as java s java math biginteger class or perl s bigint package 7 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 2466 decimal digits long a boolean type is a type that 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 four bit 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 binary coded decimal bytes and octets edit main articles byte and octet computing 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 words edit main article word computer architecture 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 bits 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 8 practically all new desktop processors are capable of using 64 bit words though embedded processors with 8 and 16 bit word size are still common the 36 bit word length was common in the early days of computers one important cause of non portability of software is the incorrect assumption that all computers have the same word size as the computer used by the programmer for example if a programmer using the c language incorrectly declares as int a variable that will be used to store values greater than 2 15 1 the program will fail on computers with 16 bit integers that variable should have been declared as long which has at least 32 bits on any computer programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information which may work on some 32 bit computers but fail on 64 bit computers with 64 bit pointers and 32 bit integers this issue is resolved by c99 in stdint h in the form of intptr_t the bitness of a program may refer to the word size or bitness of the processor on which it runs or it may refer to the width of a memory address or pointer which can differ between execution modes or contexts for example 64 bit versions of microsoft windows support existing 32 bit binaries and programs compiled for linux s x32 abi run in 64 bit mode yet use 32 bit memory addresses 9 standard integer edit the standard integer size is platform dependent in c it is denoted by int and required to be at least 16 bits windows and unix systems have 32 bit int s on both 32 bit and 64 bit architectures short integer edit a short integer can represent a whole number that may take less storage while having a smaller range compared with a standard integer on the same machine in c it is denoted by short it is required to be at least 16 bits and is often smaller than a standard integer but this is not required 10 11 a conforming program can assume that it can safely store values between 2 15 1 12 and 2 15 1 13 but it may not assume that the range is not larger in java a short is always a 16 bit integer in the windows api the datatype short is defined as a 16 bit signed integer on all machines 8 common short integer sizes programming language data type name signedness size in bytes minimum value maximum value c and c short signed 2 32 767 g 32 767 unsigned short unsigned 2 0 65 535 c short signed 2 32 768 32 767 ushort unsigned 2 0 65 535 java short signed 2 32 768 32 767 sql smallint signed 2 32 768 32 767 long integer edit a long integer can represent an integer whose range is greater than or equal to that of a standard integer on the same machine in c it is denoted by long it is required to be at least 32 bits and may or may not be larger than a standard integer a conforming program can assume that it can safely store values between 2 31 1 12 and 2 31 1 13 but it may not assume that the range is not larger common long integer sizes programming language approval type platforms data type name storage in bytes signed range unsigned range c iso ansi c99 international standard unix 16 32 bit systems 8 windows 16 32 64 bit systems 8 long 4 minimum require ment 4 2 31 1 to 2 31 1 0 to 2 32 1 minimum require ment c iso ansi c99 international standard unix 64 bit systems 8 11 long 8 minimum require ment 4 2 63 1 to 2 63 1 0 to 2 64 1 c iso ansi international standard unix windows 16 32 bit system long 4 14 minimum require ment 4 2 31 to 2 31 1 0 to 2 32 1 minimum require ment c cli international standard ecma 372 unix windows 16 32 bit systems long 4 15 minimum require ment 4 2 31 to 2 31 1 0 to 2 32 1 minimum require ment vb company standard windows long 4 16 2 31 to 2 31 1 n a vba company standard windows mac os x long 4 17 2 31 to 2 31 1 n a sql server company standard windows bigint 8 2 63 to 2 63 1 0 to 2 64 c vb net ecma international standard microsoft net long or int64 8 2 63 to 2 63 1 0 to 2 64 1 java international company standard java platform long 8 2 63 to 2 63 1 n a pascal windows unix int64 8 2 63 to 2 63 1 0 to 2 64 qword type long long edit long long redirects here for other uses see long disambiguation 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 long long type did not exist in c 03 for an ansi iso compliant compiler the minimum requirements for the specified ranges that is 2 63 1 12 to 2 63 1 for signed and 0 to 2 64 1 for unsigned 13 must be fulfilled however extending this range is permitted 18 19 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 syntax edit main article integer literal integer literals 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 i...