In
computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, ...
, endianness, also known as byte sex, is the order or sequence of
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
s of a
word
A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consen ...
of digital data in
computer memory
In computing, memory is a device or system that is used to store information for immediate use in a computer or related computer hardware and digital electronic devices. The term ''memory'' is often synonymous with the term '' primary storage ...
. Endianness is primarily expressed as big-endian (BE) or little-endian (LE). A big-endian system stores the
most significant byte of a word at the smallest
memory address
In computing, a memory address is a reference to a specific memory location used at various levels by software and hardware. Memory addresses are fixed-length sequences of digits conventionally displayed and manipulated as unsigned integers. ...
and the
least significant byte at the largest.
A little-endian system, in contrast, stores the least-significant byte at the smallest address. Bi-endianness is a feature supported by numerous computer architectures that feature switchable endianness in data fetches and stores or for instruction fetches.
Other orderings are generically called middle-endian or mixed-endian.
Endianness may also be used to describe the order in which the
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented a ...
s are transmitted over a communication channel, e.g., big-endian in a communications channel transmits the most significant bits first. Bit-endianness is seldom used in other contexts.
Etymology
Danny Cohen introduced the terms ''big-endian'' and ''little-endian'' into computer science for data ordering in an
Internet Experiment Note
An Internet Experiment Note (IEN) is a sequentially numbered document in a series of technical publications issued by the participants of the early development work groups that created the precursors of the modern Internet.
After DARPA began the ...
published in 1980.
[ Also published at '' IEEE Computer'']
October 1981 issue
The adjective ''endian'' has its origin in the writings of 18th century Anglo-Irish writer
Jonathan Swift
Jonathan Swift (30 November 1667 – 19 October 1745) was an Anglo-Irish satirist, author, essayist, political pamphleteer (first for the Whigs, then for the Tories), poet, and Anglican cleric who became Dean of St Patrick's Cathedral, ...
. In the 1726 novel ''
Gulliver's Travels
''Gulliver's Travels'', or ''Travels into Several Remote Nations of the World. In Four Parts. By Lemuel Gulliver, First a Surgeon, and then a Captain of Several Ships'' is a 1726 prose satire by the Anglo-Irish writer and clergyman Jonathan ...
'', he portrays the conflict between sects of Lilliputians divided into those breaking the shell of a
boiled egg from the big end or from the little end. He called them the ''Big-Endians'' and the ''Little-Endians''. Cohen makes the connection to ''Gulliver's Travels'' explicit in the appendix to his 1980 note.
Overview
Computers store information in various-sized groups of binary bits. Each group is assigned a number, called its ''address'', that the computer uses to access that data. On most modern computers, the smallest data group with an address is eight bits long and is called a byte. Larger groups comprise two or more bytes, for example, a
32-bit
In computer architecture, 32-bit computing refers to computer systems with a processor, memory, and other major system components that operate on data in 32- bit units. Compared to smaller bit widths, 32-bit computers can perform large calcula ...
word contains four bytes. There are two possible ways a computer could number the individual bytes in a larger group, starting at either end. Both types of endianness are in widespread use in digital electronic engineering. The initial choice of endianness of a new design is often arbitrary, but later technology revisions and updates perpetuate the existing endianness to maintain
backward compatibility
Backward compatibility (sometimes known as backwards compatibility) is a property of an operating system, product, or technology that allows for interoperability with an older legacy system, or with input designed for such a system, especially ...
.
Internally, any given computer will work equally well regardless of what endianness it uses since its hardware will consistently use the same endianness to both store and load its data. For this reason, programmers and computer users normally ignore the endianness of the computer they are working with. However, endianness can become an issue when moving data external to the computer – as when transmitting data between different computers, or a programmer investigating internal computer bytes of data from a
memory dump – and the endianness used differs from expectation. In these cases, the endianness of the data must be understood and accounted for.
These two diagrams show how two computers using different endianness store a 32-bit (four byte) integer with the value of . In both cases, the integer is broken into four bytes, , , , and , and the bytes are stored in four sequential byte locations in memory, starting with the memory location with address ''a'', then ''a + 1'', ''a + 2'', and ''a + 3''. The difference between big and little endian is the order of the four bytes of the integer being stored.
The left-side diagram shows a computer using big-endian. This starts the storing of the integer with the ''most''-significant byte, , at address ''a'', and ends with the ''least''-significant byte, , at address ''a + 3''.
The right-side diagram shows a computer using little-endian. This starts the storing of the integer with the ''least''-significant byte, , at address ''a'', and ends with the ''most''-significant byte, , at address ''a + 3''.
Since each computer uses its same endianness to both store and retrieve the integer, the results will be the same for both computers. Issues may arise when memory is addressed by bytes instead of integers, or when memory contents are transmitted between computers with different endianness.
Big-endianness is the dominant ordering in networking protocols, such as in the
internet protocol suite
The Internet protocol suite, commonly known as TCP/IP, is a framework for organizing the set of communication protocols used in the Internet and similar computer networks according to functional criteria. The foundational protocols in the sui ...
, where it is referred to as network order, transmitting the most significant byte first. Conversely, little-endianness is the dominant ordering for processor architectures (
x86, most
ARM implementations, base
RISC-V
RISC-V (pronounced "risk-five" where five refers to the number of generations of RISC architecture that were developed at the University of California, Berkeley since 1981) is an open standard instruction set architecture (ISA) based on establi ...
implementations) and their associated memory.
File format
A file format is a Computer standard, standard way that information is encoded for storage in a computer file. It specifies how bits are used to encode information in a digital storage medium. File formats may be either proprietary format, pr ...
s can use either ordering; some formats use a mixture of both or contain an indicator of which ordering is used throughout the file.
The styles of little- and big-endian may also be used more generally to characterize the ordering of any representation, e.g. the digits in a
numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
The same sequence of symb ...
or the sections of a
date. Numbers in
positional notation are generally written with their digits in left-to-right big-endian order, even in
right-to-left scripts. Similarly, programming languages use big-endian digit ordering for numeric
literals.
Basics
Computer memory
In computing, memory is a device or system that is used to store information for immediate use in a computer or related computer hardware and digital electronic devices. The term ''memory'' is often synonymous with the term '' primary storage ...
consists of a sequence of storage cells (smallest
addressable units); in machines that support
byte addressing, those units are called ''
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
s''. Each byte is identified and accessed in hardware and software by its
memory address
In computing, a memory address is a reference to a specific memory location used at various levels by software and hardware. Memory addresses are fixed-length sequences of digits conventionally displayed and manipulated as unsigned integers. ...
. If the total number of bytes in memory is ''n'', then addresses are enumerated from 0 to ''n'' − 1.
Computer programs often use data structures or
fields that may consist of more data than can be stored in one byte. In the context of this article where its type cannot be arbitrarily complicated, a "field" consists of a consecutive sequence of bytes and represents a "simple data value" which – at least potentially – can be manipulated by ''one'' single
hardware instruction. On most systems, the address of a multi-byte simple data value is the address of its first byte (the byte with the lowest address).
Another important attribute of a byte being part of a "field" is its "significance".
These attributes of the parts of a field play an important role in the sequence the bytes are accessed by the computer hardware, more precisely: by the low-level algorithms contributing to the results of a computer instruction.
Numbers
Positional number systems (mostly base 2, or less often base 10) are the predominant way of representing and particularly of manipulating
integer data by computers. In pure form this is valid for moderate sized non-negative integers, e.g. of C data type
unsigned
Unsigned can refer to:
* An unsigned artist is a musical artist or group not attached or signed to a record label
** Unsigned Music Awards, ceremony noting achievements of unsigned artists
** Unsigned band web, online community
* Similarly, the ...
. In such a number system, the ''value'' of a digit which it contributes to the whole number is determined not only by its value as a single digit, but also by the position it holds in the complete number, called its significance. These positions can be mapped to memory mainly in two ways:
* decreasing numeric significance with increasing memory addresses (or increasing time), known as ''big-endian'' and
* increasing numeric significance with increasing memory addresses (or increasing time), known as ''little-endian''.
The integer data that are directly supported by the
computer hardware have a fixed width of a low power of 2, e.g. 8 bits ≙ 1 byte, 16 bits ≙ 2 bytes, 32 bits ≙ 4 bytes, 64 bits ≙ 8 bytes, 128 bits ≙ 16 bytes. The low-level access sequence to the bytes of such a field depends on the operation to be performed. The least-significant byte is accessed first for
addition
Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or ''sum'' of ...
,
subtraction and
multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being ad ...
. The most-significant byte is accessed first for
division and
comparison. See .
For
floating-point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...
numbers, see .
Text
When character (text) strings are to be compared with one another, e.g. in order to support some mechanism like
sorting, this is very frequently done
lexicographically where a single positional element (character) also has a positional value. Lexicographical comparison means almost everywhere: first character ranks highest – as in the telephone book.
Integer numbers written as text are always represented most significant digit first in memory, which is similar to big-endian, independently of
text direction.
Hardware
Many historical and extant processors use a big-endian memory representation, either exclusively or as a design option. Other processor types use little-endian memory representation; others use yet another scheme called ''
middle-endian'', ''mixed-endian'' or ''
PDP-11
The PDP-11 is a series of 16-bit minicomputers sold by Digital Equipment Corporation (DEC) from 1970 into the 1990s, one of a set of products in the Programmed Data Processor (PDP) series. In total, around 600,000 PDP-11s of all models were so ...
-endian''.
Some instruction sets feature a setting which allows for switchable endianness in data fetches and stores, instruction fetches, or both. This feature can improve performance or simplify the logic of networking devices and software. The word ''bi-endian'', when said of hardware, denotes the capability of the machine to compute or pass data in either endian format.
Dealing with data of different endianness is sometimes termed the ''NUXI problem''. This terminology alludes to the byte order conflicts encountered while
adapting UNIX
Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, a ...
, which ran on the mixed-endian PDP-11, to a big-endian IBM Series/1 computer. Unix was one of the first systems to allow the same code to be compiled for platforms with different internal representations. One of the first programs converted was supposed to print out , but on the Series/1 it printed instead.
The
IBM System/360
The IBM System/360 (S/360) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978. It was the first family of computers designed to cover both commercial and scientific applic ...
uses big-endian byte order, as do its successors
System/370,
ESA/390, and
z/Architecture. The
PDP-10 uses big-endian addressing for byte-oriented instructions. The
IBM Series/1
The IBM Series/1 is a 16-bit minicomputer, introduced in 1976, that in many respects competed with other minicomputers of the time, such as the PDP-11 from Digital Equipment Corporation and similar offerings from Data General and HP. The S ...
minicomputer uses big-endian byte order.
The
Datapoint 2200 used simple bit-serial logic with little-endian to facilitate
carry propagation
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are ...
. When Intel developed the
8008 microprocessor for Datapoint, they used little-endian for compatibility. However, as Intel was unable to deliver the 8008 in time, Datapoint used a
medium-scale integration equivalent, but the little-endianness was retained in most Intel designs, including the
MCS-48 and the
8086
The 8086 (also called iAPX 86) is a 16-bit microprocessor chip designed by Intel between early 1976 and June 8, 1978, when it was released. The Intel 8088, released July 1, 1979, is a slightly modified chip with an external 8-bit data bus (allo ...
and its
x86 successors.
The
DEC Alpha
Alpha (original name Alpha AXP) is a 64-bit reduced instruction set computer (RISC) instruction set architecture (ISA) developed by Digital Equipment Corporation (DEC). Alpha was designed to replace 32-bit VAX complex instruction set computer ...
,
Atmel AVR
AVR is a family of microcontrollers developed since 1996 by Atmel, acquired by Microchip Technology in 2016. These are modified Harvard architecture 8-bit RISC single-chip microcontrollers. AVR was one of the first microcontroller families ...
,
VAX, the
MOS Technology 6502 family (including
Western Design Center 65802 and
65C816), the Zilog
Z80 (including
Z180 and
eZ80), the
Altera Nios II, and many other processors and processor families are also little-endian.
The Motorola
6800 / 6801, the
6809
The Motorola 6809 ("''sixty-eight-oh-nine''") is an 8-bit microprocessor with some 16-bit features. It was designed by Motorola's Terry Ritter and Joel Boney and introduced in 1978. Although source compatible with the earlier Motorola 6800, the 6 ...
and the
68000 series
The Motorola 68000 series (also known as 680x0, m68000, m68k, or 68k) is a family of 32-bit complex instruction set computer (CISC) microprocessors. During the 1980s and early 1990s, they were popular in personal computers and workstations and w ...
of processors used the big-endian format.
The Intel
8051
The Intel MCS-51 (commonly termed 8051) is a single chip microcontroller (MCU) series developed by Intel in 1980 for use in embedded systems. The architect of the Intel MCS-51 instruction set was John H. Wharton. Intel's original versions were po ...
, unlike other Intel processors, expects 16-bit addresses for LJMP and LCALL in big-endian format; however, xCALL instructions store the return address onto the stack in little-endian format.
SPARC
SPARC (Scalable Processor Architecture) is a reduced instruction set computer (RISC) instruction set architecture originally developed by Sun Microsystems. Its design was strongly influenced by the experimental Berkeley RISC system developed ...
historically used big-endian until version 9, which is
bi-endian.
Similarly early IBM POWER processors were big-endian, but the
PowerPC
PowerPC (with the backronym Performance Optimization With Enhanced RISC – Performance Computing, sometimes abbreviated as PPC) is a reduced instruction set computer (RISC) instruction set architecture (ISA) created by the 1991 Apple– IBM ...
and
Power ISA descendants are now bi-endian.
The
ARM architecture
ARM (stylised in lowercase as arm, formerly an acronym for Advanced RISC Machines and originally Acorn RISC Machine) is a family of reduced instruction set computer (RISC) instruction set architectures for computer processors, configure ...
was little-endian before version 3 when it became bi-endian.
Newer architectures
The
IA-32 and
x86-64
x86-64 (also known as x64, x86_64, AMD64, and Intel 64) is a 64-bit version of the x86 instruction set, first released in 1999. It introduced two new modes of operation, 64-bit mode and compatibility mode, along with a new 4-level paging ...
instruction set architectures use the little-endian format. Other instruction set architectures that follow this convention, allowing only little-endian mode, include
Nios II,
Andes Technology NDS32, and
Qualcomm Hexagon.
Solely big-endian architectures include the IBM
z/Architecture and
OpenRISC.
Some instruction set architectures are "bi-endian" and allow running software of either endianness; these include
Power ISA,
SPARC
SPARC (Scalable Processor Architecture) is a reduced instruction set computer (RISC) instruction set architecture originally developed by Sun Microsystems. Its design was strongly influenced by the experimental Berkeley RISC system developed ...
, ARM
AArch64,
C-Sky, and
RISC-V
RISC-V (pronounced "risk-five" where five refers to the number of generations of RISC architecture that were developed at the University of California, Berkeley since 1981) is an open standard instruction set architecture (ISA) based on establi ...
.
IBM AIX and
IBM i run in big-endian mode on bi-endian Power ISA;
Linux
Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which i ...
originally ran in big-endian mode, but by 2019, IBM had transitioned to little-endian mode for Linux to ease the porting of Linux software from x86 to Power. SPARC has no relevant little-endian deployment, as both
Oracle Solaris
Solaris is a proprietary Unix operating system originally developed by Sun Microsystems. After the Sun acquisition by Oracle in 2010, it was renamed Oracle Solaris.
Solaris superseded the company's earlier SunOS in 1993, and became known for i ...
and Linux run in big-endian mode on bi-endian SPARC systems, and can be considered big-endian in practice. ARM, C-Sky, and RISC-V have no relevant big-endian deployments, and can be considered little-endian in practice.
Bi-endianness
Some architectures (including
ARM versions 3 and above,
PowerPC
PowerPC (with the backronym Performance Optimization With Enhanced RISC – Performance Computing, sometimes abbreviated as PPC) is a reduced instruction set computer (RISC) instruction set architecture (ISA) created by the 1991 Apple– IBM ...
,
Alpha,
SPARC
SPARC (Scalable Processor Architecture) is a reduced instruction set computer (RISC) instruction set architecture originally developed by Sun Microsystems. Its design was strongly influenced by the experimental Berkeley RISC system developed ...
V9,
MIPS,
Intel i860,
PA-RISC
PA-RISC is an instruction set architecture (ISA) developed by Hewlett-Packard. As the name implies, it is a reduced instruction set computer (RISC) architecture, where the PA stands for Precision Architecture. The design is also referred to a ...
,
SuperH SH-4 and
IA-64
IA-64 (Intel Itanium architecture) is the instruction set architecture (ISA) of the Itanium family of 64-bit Intel microprocessors. The basic ISA specification originated at Hewlett-Packard (HP), and was subsequently implemented by Intel in col ...
) feature a setting which allows for switchable endianness in data fetches and stores, instruction fetches, or both. This feature can improve performance or simplify the logic of networking devices and software. The word ''bi-endian'', when said of hardware, denotes the capability of the machine to compute or pass data in either endian format.
Many of these architectures can be switched via software to default to a specific endian format (usually done when the computer starts up); however, on some systems, the default endianness is selected by hardware on the motherboard and cannot be changed via software (e.g. the Alpha, which runs only in big-endian mode on the
Cray T3E
The Cray T3E was Cray Research's second-generation massively parallel supercomputer architecture, launched in late November 1995. The first T3E was installed at the Pittsburgh Supercomputing Center in 1996. Like the previous Cray T3D, it was a ful ...
).
Note that the term ''bi-endian'' refers primarily to how a processor treats data accesses. Instruction accesses (fetches of instruction words) on a given processor may still assume a fixed endianness, even if data accesses are fully bi-endian, though this is not always the case, such as on Intel's
IA-64
IA-64 (Intel Itanium architecture) is the instruction set architecture (ISA) of the Itanium family of 64-bit Intel microprocessors. The basic ISA specification originated at Hewlett-Packard (HP), and was subsequently implemented by Intel in col ...
-based Itanium CPU, which allows both.
Note, too, that some nominally bi-endian CPUs require motherboard help to fully switch endianness. For instance, the 32-bit desktop-oriented
PowerPC
PowerPC (with the backronym Performance Optimization With Enhanced RISC – Performance Computing, sometimes abbreviated as PPC) is a reduced instruction set computer (RISC) instruction set architecture (ISA) created by the 1991 Apple– IBM ...
processors in little-endian mode act as little-endian from the point of view of the executing programs, but they require the motherboard to perform a 64-bit swap across all 8 byte lanes to ensure that the little-endian view of things will apply to
I/O devices. In the absence of this unusual motherboard hardware, device driver software must write to different addresses to undo the incomplete transformation and also must perform a normal byte swap.
Some CPUs, such as many PowerPC processors intended for embedded use and almost all SPARC processors, allow per-page choice of endianness.
SPARC processors since the late 1990s (SPARC v9 compliant processors) allow data endianness to be chosen with each individual instruction that loads from or stores to memory.
The
ARM architecture
ARM (stylised in lowercase as arm, formerly an acronym for Advanced RISC Machines and originally Acorn RISC Machine) is a family of reduced instruction set computer (RISC) instruction set architectures for computer processors, configure ...
supports two big-endian modes, called ''BE-8'' and ''BE-32''. CPUs up to ARMv5 only support BE-32 or word-invariant mode. Here any naturally aligned 32-bit access works like in little-endian mode, but access to a byte or 16-bit word is redirected to the corresponding address and unaligned access is not allowed. ARMv6 introduces BE-8 or byte-invariant mode, where access to a single byte works as in little-endian mode, but accessing a 16-bit, 32-bit or (starting with ARMv8) 64-bit word results in a byte swap of the data. This simplifies unaligned memory access as well as memory-mapped access to registers other than 32 bit.
Many processors have instructions to convert a word in a register to the opposite endianness, that is, they swap the order of the bytes in a 16-, 32- or 64-bit word. All the individual bits are not reversed though.
Recent Intel x86 and x86-64 architecture CPUs have a MOVBE instruction (
Intel Core
Intel Core is a line of streamlined midrange consumer, workstation and enthusiast computer central processing units (CPUs) marketed by Intel Corporation. These processors displaced the existing mid- to high-end Pentium processors at the time ...
since generation 4, after
Atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas ...
), which fetches a big-endian format word from memory or writes a word into memory in big-endian format. These processors are otherwise thoroughly little-endian.
There are also devices which use different formats in different places. For instance, the BQ27421
Texas Instruments
Texas Instruments Incorporated (TI) is an American technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globa ...
battery gauge uses the little-endian format for its registers and the big-endian format for its
random-access memory
Random-access memory (RAM; ) is a form of computer memory that can be read and changed in any order, typically used to store working data and machine code. A random-access memory device allows data items to be read or written in almost t ...
. This behavior does not seem to be modifiable.
Floating point
Although many processors use little-endian storage for all types of data (integer, floating point), there are a number of hardware architectures where
floating-point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...
numbers are represented in big-endian form while integers are represented in little-endian form. There are
ARM processors that have mixed-endian floating-point representation for double-precision numbers: each of the two 32-bit words is stored as little-endian, but the most significant word is stored first.
VAX floating point stores little-endian 16-bit words in big-endian order. Because there have been many floating-point formats with no network standard representation for them, the
XDR standard uses big-endian IEEE 754 as its representation. It may therefore appear strange that the widespread
IEEE 754 floating-point standard does not specify endianness. Theoretically, this means that even standard IEEE floating-point data written by one machine might not be readable by another. However, on modern standard computers (i.e., implementing IEEE 754), one may safely assume that the endianness is the same for floating-point numbers as for integers, making the conversion straightforward regardless of data type. Small
embedded system
An embedded system is a computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated function within a larger mechanical or electronic system. It is ''embedded'' ...
s using special floating-point formats may be another matter, however.
Variable-length data
Most instructions considered so far contain the size (lengths) of their
operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on.
Example
The following arithmetic expression shows an example of operators and operands:
:3 + 6 = 9
In the above exa ...
s within the
operation code
In computing, an opcode (abbreviated from operation code, also known as instruction machine code, instruction code, instruction syllable, instruction parcel or opstring) is the portion of a machine language instruction that specifies the operat ...
. Frequently available operand lengths are 1, 2, 4, 8, or 16 bytes. But there are also architectures where the length of an operand may be held in a separate field of the instruction or with the operand itself, e.g. by means of a
word mark
__notoc__
A wordmark, word mark, or logotype, is usually a distinct text-only typographic treatment of the name of a company, institution, or product name used for purposes of identification and branding. Examples can be found in the graphic iden ...
. Such an approach allows operand lengths up to 256 bytes or larger. The data types of such operands are
character strings or
BCD. Machines able to manipulate such data with one instruction (e.g. compare, add) include the
IBM 1401
The IBM 1401 is a variable-wordlength decimal computer that was announced by IBM on October 5, 1959. The first member of the highly successful IBM 1400 series, it was aimed at replacing unit record equipment for processing data stored on pu ...
,
1410
Year 1410 ( MCDX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar.
Events
January–December
* March 25 – The first of the Yongle Emperor's campaigns against the Mongols is ...
,
1620
Events
January–June
* February 4 – Prince Bethlen Gabor signs a peace treaty with Ferdinand II, Holy Roman Emperor.
* May 17 – The first merry-go-round is seen at a fair (Philippapolis, Turkey).
* June 3 – The ...
,
System/360
The IBM System/360 (S/360) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978. It was the first family of computers designed to cover both commercial and scientific applic ...
,
System/370,
ESA/390, and
z/Architecture, all of them of type big-endian.
Simplified access to part of a field
On most systems, the address of a multi-byte value is the address of its first byte (the byte with the lowest address); little-endian systems of that type have the property that, for sufficiently low data values, the same value can be read from memory at different lengths without using different addresses (even when
alignment restrictions are imposed). For example, a 32-bit memory location with content can be read at the same address as either
8-bit
In computer architecture, 8-bit integers or other data units are those that are 8 bits wide (1 octet). Also, 8-bit central processing unit (CPU) and arithmetic logic unit (ALU) architectures are those that are based on registers or data buses of ...
(value = 4A),
16-bit (004A),
24-bit (00004A), or
32-bit
In computer architecture, 32-bit computing refers to computer systems with a processor, memory, and other major system components that operate on data in 32- bit units. Compared to smaller bit widths, 32-bit computers can perform large calcula ...
(0000004A), all of which retain the same numeric value. Although this little-endian property is rarely used directly by high-level programmers, it is occasionally employed by code optimizers as well as by
assembly language programmers.
In more concrete terms, identities like this are the equivalent of the following
C code returning ''true'' on most little-endian systems:
union u = ;
puts(u.u8 u.u16 && u.u8 u.u32 && u.u8 u.u64 ? "true" : "false");
While not allowed by C++, such
type punning
In computer science, a type punning is any programming technique that subverts or circumvents the type system of a programming language in order to achieve an effect that would be difficult or impossible to achieve within the bounds of the formal ...
code is allowed as "implementation-defined" by the C11 standard and commonly used in code interacting with hardware.
On the other hand, in some situations it may be useful to obtain an approximation of a multi-byte or multi-word value by reading only its most significant portion instead of the complete representation; a big-endian processor may read such an approximation using the same base address that would be used for the full value.
Simplifications of this kind are of course not portable across systems of different endianness.
Calculation order
Some operations in
positional number system
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...
s have a natural or preferred order in which the elementary steps are to be executed. This order may affect their performance on small-scale byte-addressable processors and
microcontroller
A microcontroller (MCU for ''microcontroller unit'', often also MC, UC, or μC) is a small computer on a single VLSI integrated circuit (IC) chip. A microcontroller contains one or more CPUs ( processor cores) along with memory and programma ...
s. However, high-performance processors usually fetch multi-byte operands from memory in the same amount of time they would have fetched a single byte, so the complexity of the hardware is not affected by the byte ordering.
Addition, subtraction, and multiplication start at the least significant digit position and
propagate the carry to the subsequent more significant position. On most systems, the address of a multi-byte value is the address of its first byte (the byte with the lowest address). The implementation of these operations is marginally simpler using little-endian machines where this first byte contains the least significant digit.
Comparison and division start at the most significant digit and propagate a possible carry to the subsequent less significant digits. For fixed-length numerical values (typically of length 1,2,4,8,16), the implementation of these operations is marginally simpler on big-endian machines.
Some big-endian processors (e.g. the IBM System/360 and its successors) contain hardware instructions for lexicographically comparing varying length character strings.
The normal data transport by an
assignment statement is in principle independent of the endianness of the processor.
Middle-endian
Numerous other orderings, generically called ''middle-endian'' or ''mixed-endian'', are possible.
The
PDP-11
The PDP-11 is a series of 16-bit minicomputers sold by Digital Equipment Corporation (DEC) from 1970 into the 1990s, one of a set of products in the Programmed Data Processor (PDP) series. In total, around 600,000 PDP-11s of all models were so ...
is in principle a 16-bit little-endian system. The instructions to convert between floating-point and integer values in the optional floating-point processor of the PDP-11/45, PDP-11/70, and in some later processors, stored 32-bit "double precision integer long" values with the 16-bit halves swapped from the expected little-endian order. The
UNIX
Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, a ...
C compiler used the same format for 32-bit long integers. This ordering is known as ''PDP-endian''.
A way to interpret this endianness is that it stores a 32-bit integer as two little-endian 16-bit words, with a big-endian word ordering:
The 16-bit values here refer to their numerical values, not their actual layout.
Segment descriptors of
IA-32 and compatible processors keep a 32-bit base address of the segment stored in little-endian order, but in four nonconsecutive bytes, at relative positions 2, 3, 4 and 7 of the descriptor start.
Endian dates
Dates can be represented with different endianness by the ordering of the year, month and day. For example, September 13, 2002 can be represented as:
* little-endian date (day, month, year),
* middle-endian dates (month, day, year),
* big-endian date (year, month, day), as with
ISO 8601
ISO 8601 is an international standard covering the worldwide exchange and communication of date and time-related data. It is maintained by the Geneva-based International Organization for Standardization (ISO) and was first published in 1988, ...
In
date and time notation in the United States, dates are middle-endian and differ from
date formats worldwide.
Byte addressing
When memory bytes are printed sequentially from left to right (e.g. in a
hex dump), little-endian representation of integers has the significance increasing from left to right. In other words, it appears backwards when visualized, which can be counter-intuitive.
This behavior arises, for example, in
FourCC or similar techniques that involve packing characters into an integer, so that it becomes a sequences of specific characters in memory. Let's define the notation as simply the result of writing the characters in hexadecimal
ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
and appending to the front, and analogously for shorter sequences (a
C multicharacter literal, in Unix/MacOS style):
' J o h n '
hex 4A 6F 68 6E
----------------
-> 0x4A6F686E
On big-endian machines, the value appears left-to-right, coinciding with the correct string order for reading the result:
But on a little-endian machine, one would see:
Middle-endian machines complicate this even further; for example, on the
PDP-11
The PDP-11 is a series of 16-bit minicomputers sold by Digital Equipment Corporation (DEC) from 1970 into the 1990s, one of a set of products in the Programmed Data Processor (PDP) series. In total, around 600,000 PDP-11s of all models were so ...
, the 32-bit value is stored as two 16-bit words in big-endian, with the characters in the 16-bit words being stored in little-endian:
Byte swapping
Byte-swapping consists of rearranging bytes to change endianness. Many compilers provide
built-ins that are likely to be compiled into native processor instructions (/), such as . Software interfaces for swapping include:
* Standard
network endianness functions (from/to BE, up to 32-bit). Windows has a 64-bit extension in .
* BSD and Glibc functions (from/to BE and LE, up to 64-bit).
*
macOS
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac (computer), Mac computers. Within the market of ...
macros (from/to BE and LE, up to 64-bit).
Some
CPU
A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, and ...
instruction sets provide native support for endian byte swapping, such as (
x86 -
486
__NOTOC__
Year 486 ( CDLXXXVI) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Basilius and Longinus (or, less frequently, year 12 ...
and later), and (
ARMv6 and later).
Some
compiler
In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that ...
s have built-in facilities for byte swapping. For example, the
Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the devel ...
Fortran compiler supports the non-standard specifier when opening a file, e.g.: . Other compilers have options for generating code that globally enables the conversion for all file IO operations. This permits the reuse of code on a system with the opposite endianness without code modification.
Logic design
Hardware description languages (HDLs) used to express digital logic often support arbitrary endianness, with arbitrary granularity. For example, in
SystemVerilog, a word can be defined as little endian or big endian:
logic 1:0little_endian; // bit 0 is the least significant bit
logic :31big_endian; // bit 31 is the least significant bit
logic :37:0] mixed; // each byte is little-endian, but bytes are packed in big-endian order.
Files and filesystems
The recognition of endianness is important when reading a file or filesystem created on a computer with different endianness.
Fortran sequential unformatted files created with one endianness usually cannot be read on a system using the other endianness because Fortran usually implements a
storage record, record (defined as the data written by a single Fortran statement) as data preceded and succeeded by count fields, which are integers equal to the number of bytes in the data. An attempt to read such a file using Fortran on a system of the other endianness results in a run-time error, because the count fields are incorrect.
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
text can optionally start with a
byte order mark
The byte order mark (BOM) is a particular usage of the special Unicode character, , whose appearance as a magic number at the start of a text stream can signal several things to a program reading the text:
* The byte order, or endianness, of ...
(BOM) to signal the endianness of the file or stream. Its code point is U+FEFF. In
UTF-32 for example, a big-endian file should start with ; a little-endian should start with .
Application binary data formats, such as
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...
''.mat'' files, or the ''.bil'' data format, used in topography, are usually endianness-independent. This is achieved by storing the data always in one fixed endianness or carrying with the data a switch to indicate the endianness. An example of the former is the binary
XLS file format that is portable between Windows and Mac systems and always little-endian, requiring the Mac application to swap the bytes on load and save when running on a big-endian Motorola 68K or PowerPC processor.
TIFF
Tag Image File Format, abbreviated TIFF or TIF, is an image file format for storing raster graphics images, popular among graphic artists, the publishing industry, and photographers. TIFF is widely supported by scanning, faxing, word processin ...
image files are an example of the second strategy, whose header instructs the application about endianness of their internal binary integers. If a file starts with the signature it means that integers are represented as big-endian, while means little-endian. Those signatures need a single 16-bit word each, and they are
palindromes (that is, they read the same forwards and backwards), so they are endianness independent. stands for
Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the devel ...
and stands for
Motorola
Motorola, Inc. () was an American multinational telecommunications company based in Schaumburg, Illinois, United States. After having lost $4.3 billion from 2007 to 2009, the company split into two independent public companies, Motorola ...
, the respective
CPU
A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, and ...
providers of the
IBM PC compatibles (Intel) and
Apple Macintosh
The Mac (known as Macintosh until 1999) is a family of personal computers designed and marketed by Apple Inc. Macs are known for their ease of use and minimalist designs, and are popular among students, creative professionals, and software ...
platforms (Motorola) in the 1980s. Intel CPUs are little-endian, while Motorola 680x0 CPUs are big-endian. This explicit signature allows a TIFF reader program to swap bytes if necessary when a given file was generated by a TIFF writer program running on a computer with a different endianness.
As a consequence of its original implementation on the Intel 8080 platform, the operating system-independent
File Allocation Table (FAT) file system is defined with little-endian byte ordering, even on platforms using another endianness natively, necessitating byte-swap operations for maintaining the FAT.
ZFS, which combines a
filesystem
In computing, file system or filesystem (often abbreviated to fs) is a method and data structure that the operating system uses to control how data is stored and retrieved. Without a file system, data placed in a storage medium would be one larg ...
and a
logical volume manager, is known to provide adaptive endianness and to work with both big-endian and little-endian systems.
Networking
Many
IETF RFCs use the term ''network order'', meaning the order of transmission for bits and bytes ''over the wire'' in
network protocols. Among others, the historic RFC 1700 (also known as
Internet standard STD 2) has defined the network order for protocols in the
Internet protocol suite
The Internet protocol suite, commonly known as TCP/IP, is a framework for organizing the set of communication protocols used in the Internet and similar computer networks according to functional criteria. The foundational protocols in the sui ...
to be big-endian, hence the use of the term for big-endian byte order.
However, not all protocols use big-endian byte order as the network order. The
Server Message Block (SMB) protocol uses little-endian byte order. In
CANopen, multi-byte parameters are always sent
least significant byte first (little-endian). The same is true for
Ethernet Powerlink
Ethernet Powerlink is a real-time protocol for standard Ethernet. It is an open protocol managed by the Ethernet POWERLINK Standardization Group (EPSG). It was introduced by Austrian automation company B&R in 2001.
This protocol has nothing to ...
.
The
Berkeley sockets API defines a set of functions to convert 16-bit and 32-bit integers to and from network byte order: the (host-to-network-short) and (host-to-network-long) functions convert 16-bit and 32-bit values respectively from machine (''host'') to network order; the and functions convert from network to host order. These functions may be a
no-op
In computer science, a NOP, no-op, or NOOP (pronounced "no op"; short for no operation) is a machine language instruction and its assembly language mnemonic, programming language statement, or computer protocol command that does nothing.
...
on a big-endian system.
While the high-level network protocols usually consider the byte (mostly meant as ''
octet
Octet may refer to:
Music
* Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble
** String octet, a piece of music written for eight string instruments
*** Octet (Mendelssohn), 1825 com ...
'') as their atomic unit, the lowest network protocols may deal with ordering of bits within a byte.
Bit endianness
Bit numbering is a concept similar to endianness, but on a level of bits, not bytes. Bit endianness or bit-level endianness refers to the transmission order of bits over a serial medium. The bit-level analogue of little-endian (least significant bit goes first) is used in
RS-232
In telecommunications, RS-232 or Recommended Standard 232 is a standard originally introduced in 1960 for serial communication transmission of data. It formally defines signals connecting between a ''DTE'' ('' data terminal equipment'') suc ...
,
HDLC,
Ethernet
Ethernet () is a family of wired computer networking technologies commonly used in local area networks (LAN), metropolitan area networks (MAN) and wide area networks (WAN). It was commercially introduced in 1980 and first standardized in ...
, and
USB. Some protocols use the opposite ordering (e.g.
Teletext
A British Ceefax football index page from October 2009, showing the three-digit page numbers for a variety of football news stories
Teletext, or broadcast teletext, is a standard for displaying text and rudimentary graphics on suitably equipp ...
,
I2C,
SMBus,
PMBus, and
SONET and SDH[Cf. Sec. 2.1 Bit Transmission o]
draft-ietf-pppext-sonet-as-00 "Applicability Statement for PPP over SONET/SDH"
/ref>), and ARINC 429 uses one ordering for its label field and the other ordering for the remainder of the frame. Usually, there exists a consistent view to the bits irrespective of their order in the byte, such that the latter becomes relevant only on a very low level. One exception is caused by the feature of some cyclic redundancy checks to detect ''all'' burst errors up to a known length, which would be spoiled if the bit order is different from the byte order on serial transmission.
Apart from serialization, the terms ''bit endianness'' and ''bit-level endianness'' are seldom used, as computer architectures where each individual bit has a unique address are rare. Individual bits or bit fields are accessed via their numerical value or, in high-level programming languages, assigned names, the effects of which, however, may be machine dependent or lack software portability
A computer program is said to be portable if there is very low effort required to make it run on different platforms. The pre-requirement for portability is the generalized abstraction between the application logic and system interfaces. When ...
.
Notes
References
{{Reflist
Computer memory
Data transmission
Metaphors
Software wars