Endianness

In computing, endianness refers to the order of bytes (or sometimes bits) within a binary representation of a number. It can also be used more generally to refer to the internal ordering of any representation, such as the digits in a numeral system or the sections of a date.

In its most common usage, endianness indicates the ordering of bytes within a multi-byte number. A little-endian ordering places the least significant byte first and the most significant byte last, while a big-endian ordering does the opposite. For example, consider the unsigned hexadecimal number 0x1234, which requires at least two bytes to represent. In a little-endian ordering, the bytes would be arranged [ 0x34, 0x12 ], while in a big-endian ordering they would be [ 0x12, 0x34 ].

Historically, various methods of endianness have been used in computing, including exotic forms such as middle-endianness. Today, however, little-endianness is the dominant ordering for processor architectures (x86, most ARM implementations) and their associated memory. Conversely, big-endianness is the dominant ordering in networking protocols (IP, TCP, UDP). File formats can use either ordering; some formats use a mixture of both.

In left-to-right scripts, numbers are written with their digits in big-endian order. Similarly, programming languages use big-endian digit ordering for numeric literals as well as big-endian language (“left” and “right”) for bit-shift operations, regardless of the endianness of the target architecture; this can lead to confusion when interacting with little-endian numbers.

Illustration[edit]

The following two descriptive illustrations assume a normal reading and writing convention of left to right, where the left-most digit or character therefore corresponds to data being sent or received first, or being in the lowest address in memory, and the right-most digit or character corresponds to the data being sent or received last, or being in the highest address in memory.

Big-endianness may be demonstrated by writing a decimal number, say one hundred twenty-three, on paper in the usual positional notation understood by a numerate reader: 123; the digits are written starting from the left and to the right, with the most significant digit, 1, written first. This is analogous to the lowest address of memory being used first; this is an example of a big-endian convention taken from daily life.

The little-endian way of writing the same number, one hundred twenty-three, would place the hundreds-digit 1 in the right-most position: 321. A person following conventional big-endian place-value order, who is not aware of this special ordering, would read a different number: three hundred and twenty one. Endianness in computing is similar, but it usually applies to the ordering of bytes, rather than of digits.

The illustrations to the right, where a is a memory address, show big-endian and little-endian storage in memory.

Etymology[edit]

Danny Cohen introduced the terms Little-Endian and Big-Endian for byte ordering in an article published by the Internet Engineering Task Force (IETF) in 1980.^[1][2] In this technical and political examination of byte ordering issues, the endian names were drawn from Jonathan Swift's 1726 satire, Gulliver's Travels, in which civil war erupts over whether the big end or the little end of a boiled egg is the proper end to crack open, which is analogous to counting from the end that contains the most significant bit or the least significant bit.^[3][4]

Hardware[edit]

Computer memory consists of a sequence of storage cells; each cell is identified in hardware and software by its memory address. If the total number of storage cells in memory is n, then addresses are enumerated from 0 to n-1. Computer programs often use data structures of fields that may consist of more data than is stored in one memory cell. For the purpose of this article where its use as an operand of an instruction is relevant, a field consists of a consecutive sequence of bytes and represents a simple data value. In addition to that, it has to be of numeric type in some positional number system (mostly base-10 or base-2 – or base-256 in case of 8-bit bytes).^[5] In such a number system the "value" of a digit is determined not only by its value as a single digit, but also by the position it holds in the complete number, its "significance"; these positions can be mapped to memory mainly in two ways:^[6]

• increasing numeric significance with increasing memory addresses (or increasing time), known as little-endian, and
• decreasing numeric significance with increasing memory addresses (or increasing time), known as big-endian^[7]

History[edit]

While the little-endian Intel microprocessor product line became a popular architecture, many historical and extant processors use a big-endian memory representation, commonly referred to as network order, as used in the Internet protocol suite, either exclusively or as a design option; others use yet another scheme called "middle-endian", "mixed-endian" or "PDP-11-endian".

The IBM System/360 uses big-endian byte order, as do its successors System/370, ESA/390, and z/Architecture; the PDP-10 also uses big-endian addressing for byte-oriented instructions. The IBM Series/1 minicomputer also use big-endian byte order.

Dealing with data of different endianness is sometimes termed the NUXI problem;^[8] this terminology alludes to the byte order conflicts encountered while adapting UNIX, 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 Unix, but on the Series/1 it printed nUxi instead.^[9]

The Datapoint 2200 uses simple bit-serial logic with little-endian to facilitate carry propagation; 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 and its x86 successors;^[10][11] the DEC Alpha, Atmel AVR, 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 and the 68000 series of processors used the big-endian format.

The Intel 8051, contrary to 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.^[12]

SPARC historically used big-endian until version 9, which is bi-endian; similarly early IBM POWER processors were big-endian, but now the PowerPC and Power ISA descendants are bi-endian; the ARM architecture was little-endian before version 3 when it became bi-endian.

Current architectures[edit]

The Intel x86 and also AMD64 / x86-64 series of processors use the little-endian format. Recently designed instruction set architectures typically follow this convention, either allowing only little-endian mode (e.g. RISC-V, Nios II, Andes Technology NDS32, or Qualcomm Hexagon), or running mostly little-endian software on a bi-endian architecture (e.g. ARM Aarch64, C-Sky).

Some big-endian architectures that remain popular include mostly older examples like the IBM z/Architecture, Freescale ColdFire (which is Motorola 68000 series-based) and Atmel AVR32, but also the more recent OpenRISC; the IBM AIX and Oracle Solaris operating systems on bi-endian Power ISA and SPARC run in big-endian mode, while Linux on Power has moved to little-endian mode for new distributions.

Bi-endianness[edit]

Some architectures (including ARM versions 3 and above, PowerPC, Alpha, SPARC V9, MIPS, PA-RISC, SuperH SH-4 and IA-64) 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).

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-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 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 supports two big-endian modes, called BE-8 and BE-32.^[13] 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. With ARMv7 and later, only BE-8 mode is allowed.^{[clarification needed]}

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 since generation 4, after Atom),^[14] 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. They also already had a range of swap instructions to reverse the byte order of the contents of registers, such as when words have already been fetched from memory locations where they were in the 'wrong' endianness.

Floating point[edit]

Although the ubiquitous x86 processors of today use little-endian storage for all types of data (integer, floating point, BCD), there are a number of hardware architectures where floating-point numbers are represented in big-endian form while integers are represented in little-endian form.^[15] There are ARM processors that have half little-endian, half big-endian floating-point representation for double-precision numbers: both 32-bit words are stored in little-endian like integer registers, but the most significant one first; 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.^[16] 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 in practice 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 systems using special floating-point formats may be another matter however.)

Optimization[edit]

The little-endian system has the property that 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 4A 00 00 00 can be read at the same address as either 8-bit (value = 4A), 16-bit (004A), 24-bit (00004A), or 32-bit (0000004A), all of which retain the same numeric value. Although this little-endian property is rarely used directly by high-level programmers, it is often employed by code optimizers as well as by assembly language programmers. In more concrete terms, such optimizations are the equivalent of the following C code returning true on most little-endian systems:

union u_t {
  uint8_t u8; uint16_t u16; uint32_t u32; uint64_t u64;
} u = { .u64 = 0x4A };
puts(u.u8 == u.u16 && u.u8 == u.u32 && u.u8 == u.u64 ? "true" : "false");

While not allowed by C++, such Type punning code is allowed as "implementation-defined" by the C11 standard^[17] and commonly used^[18] in code interacting with hardware.^[19]

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.

Optimizations of this kind are not portable across systems of different endianness.

Calculation order[edit]

Little-endian representation simplifies hardware in processors that add multi-byte integral values a byte at a time, such as small-scale byte-addressable processors and microcontrollers; as carry propagation must start at the least significant bit (and thus byte), multi-byte addition can then be carried out with a monotonically-incrementing address sequence, a simple operation already present in hardware. On a big-endian processor, its addressing unit has to be told how big the addition is going to be so that it can hop forward to the least significant byte, then count back down towards the most significant byte (MSB). On the other hand, arithmetic division is done starting from the MSB, so it is more natural for big-endian processors. However, high-performance processors usually fetch typical 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.

Mapping multi-byte binary values to memory[edit]

We can assume that as we write text left to right, we are increasing the 'address' on paper, as a processor would write bytes with increasing memory addresses — as in the adjacent table. On paper, the hex value 0a0b0c0d (written 168496141 in usual decimal notation) is big-endian style since we write the most significant digit first and the rest follow in decreasing significance. Mapping this number as a binary value to a sequence of 4 bytes in memory in big-endian style also writes the bytes from left to right in decreasing significance: 0A_h at +0, 0B_h at +1, 0C_h at +2, 0D_h at +3.

On a little-endian system, the bytes are written from left to right in increasing significance, starting with the one's byte: 0D_h at +0, 0C_h at +1, 0B_h at +2, 0A_h at +3. Writing a 32-bit binary value to a memory location on a little-endian system and outputting the memory location (with growing addresses from left to right) shows that the order is reversed (byte-swapped) compared to usual big-endian notation; this is the way a hexdump is displayed: because the dumping program is unable to know what kind of data it is dumping, the only orientation it can observe is monotonically increasing addresses. The human reader, however, who knows that they are reading a hexdump of a little-endian system and who knows what kind of data they are reading, reads the byte sequence 0D_h,0C_h,0B_h,0A_h as the 32-bit binary value 168496141, or 0x0a0b0c0d in hexadecimal notation. (Of course, this is not the same as the number 0D0C0B0A_h = 0x0d0c0b0a = 218893066.)

Examples[edit]

This section provides example layouts of the 32-bit number 0A0B0C0D_h in the most common variants of endianness. There exist several digital processors that use other formats; that is true for typical embedded systems as well as for general computer CPUs. Most processors used in non CPU roles in typical computers (in storage units, peripherals etc.) also use one of these two basic formats, although not always 32-bit.

The examples refer to the storage in memory of the value, it uses hexadecimal notation.

Big-endian[edit]

Atomic element size 8-bit[edit]

address increment 1-byte (octet)

The most significant byte (MSB) value, 0A_h, is at the lowest address. The other bytes follow in decreasing order of significance; this is akin to left-to-right reading in hexadecimal order.

Atomic element size 16-bit[edit]

The most significant atomic element stores now the value 0A0B_h, followed by 0C0D_h.

Little-endian[edit]

Atomic element size 8-bit[edit]

address increment 1-byte (octet)

The least significant byte (LSB) value, 0D_h, is at the lowest address. The other bytes follow in increasing order of significance; this is akin to right-to-left reading in hexadecimal order.

Atomic element size 16-bit[edit]

The least significant 16-bit unit stores the value 0C0D_h, immediately followed by 0A0B_h. Note that 0C0D_h and 0A0B_h represent integers, not bit layouts.^{[clarification needed]}

When organized by byte addresses[edit]

Byte addresses increasing from right to left

Visualising memory addresses from left to right makes little-endian values appear backwards. If the addresses are written increasing towards the left instead, each individual little-endian value will appear forwards; however strings of values or characters appear reversed instead.

With 8-bit atomic elements:

The least significant byte (LSB) value, 0D_h, is at the lowest address. The other bytes follow in increasing order of significance.

With 16-bit atomic elements:

The least significant 16-bit unit stores the value 0C0D_h, immediately followed by 0A0B_h.

The display of text is reversed from the normal display of languages such as English that read from left to right. For example, the word "XRAY" displayed in this manner, with each character stored in an 8-bit atomic element:

If pairs of characters are stored in 16-bit atomic elements (using 8 bits per character), it could look even stranger:

This conflict between the memory arrangements of binary data and text is intrinsic to the nature of the little-endian convention, but is a conflict only for languages written left-to-right, such as English. For right-to-left languages such as Arabic and Hebrew, there is no conflict of text with binary, and the preferred display in both cases would be with addresses increasing to the left. (On the other hand, right-to-left languages have a complementary intrinsic conflict in the big-endian system.)

Middle-endian[edit]

Numerous other orderings, generically called middle-endian or mixed-endian, are possible, such as the standard American date formatting of month/day/year.

On the PDP-11 (16-bit little-endian), for example, the instructions to convert between floating-point and integer values in the optional floating-point processor on the PDP-11/45^[20] and 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, and the UNIX C compiler used the same format for 32-bit long integers; this ordering is known as PDP-endian.

• storage of a 32-bit word (hexadecimal 0A0B0C0D) on a PDP-11

The ARM architecture can also produce this format when writing a 32-bit word to an address 2 bytes from a 32-bit word alignment.

Segment descriptors on Intel 80386 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.

A C programming example[edit]

Consider the following C language program:

    #include <stdio.h>
    int main(void) {                                                                                                                              
      union {
        unsigned int word;  // a 32-bit integer
        unsigned char bytes[4];
      } u;
                                                                                                                                          
      u.word = 0x0A0B0C0D;
      for (int i = 0; i < 4; i++) {
        printf("byte[%d] = 0x%x\n", i, (int)u.bytes[i]);
      }
    }

On a little-endian computer, this program would output:

   byte[0] = 0xd
   byte[1] = 0xc
   byte[2] = 0xb
   byte[3] = 0xa

On a big-endian computer, this program would output:

   byte[0] = 0xa
   byte[1] = 0xb
   byte[2] = 0xc
   byte[3] = 0xd

Files and byte swap[edit]

Endianness is a problem when a binary file created on a computer is read on another computer with different endianness; some CPU instruction sets provide native support for endian byte swapping, such as bswap^[21] (x86 - 486 and later), and rev^[22] (ARMv6 and later).

Some compilers have built-in facilities to deal with data written in other formats. For example, the Intel Fortran compiler supports the non-standard CONVERT specifier, so a file can be opened as

OPEN(unit,CONVERT='BIG_ENDIAN',...)

or

OPEN(unit,CONVERT='LITTLE_ENDIAN',...)

Some compilers have options to generate code that globally enables the conversion for all file IO operations; this allows programmers to reuse code on a system with the opposite endianness without having to modify the code itself. If the compiler does not support such conversion, the programmer needs to swap the bytes via ad hoc code.

Fortran sequential unformatted files created with one endianness usually cannot be read on a system using the other endianness because Fortran usually implements a 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 file on a system of the other endianness then results in a run-time error, because the count fields are incorrect; this problem can be avoided by writing out sequential binary files as opposed to sequential unformatted.

Unicode text can optionally start with a byte order mark (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 00 00 FE FF; a little-endian should start with FF FE 00 00.

Application binary data formats, such as for example MATLAB .mat files, or the .BIL data format, used in topography, are usually endianness-independent; this is achieved by:

1. storing the data always in one fixed endianness, or
2. carrying with the data a switch to indicate which endianness the data was written with.

When reading the file, the application converts the endianness, invisibly from the user. An example of the first case is the binary XLS file format that is portable between Windows and Mac systems and always little-endian, leaving the Mac application to swap the bytes on load and save when running on a big-endian Motorola 68K or PowerPC processor.^[23]

TIFF 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 "MM" it means that integers are represented as big-endian, while "II" 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. "I" stands for Intel and "M" stands for Motorola, the respective CPU providers of the IBM PC compatibles (Intel) and Apple Macintosh 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.

Since the required byte swap depends on the size of the numbers stored in the file (two 2-byte integers require a different swap than one 4-byte integer), the file format must be known to perform endianness conversion.

/* C function to change endianness for byte swap in an unsigned 32-bit integer */

uint32_t ChangeEndianness(uint32_t value)
{
    uint32_t result = 0;
    result |= (value & 0x000000FF) << 24;
    result |= (value & 0x0000FF00) << 8;
    result |= (value & 0x00FF0000) >> 8;
    result |= (value & 0xFF000000) >> 24;
    return result;
}

File systems[edit]

Endianness is also a problem when a file system created on a computer is processed on another computer with different endianness, because the values in the data structures maintained on the file system on secondary storage may be written in the endianness of the machine that created the file system.

As a consequence of its original implementation on the Intel 8080 platform, the operating system-independent FAT file system is defined to use little-endian byte ordering, even on platforms using other endiannesses natively, so code to read and write FAT file systems must byte-swap multi-byte values on non-little-endian processors.

ZFS/OpenZFS combined file system and logical volume manager is known to provide adaptive endianness and to work with both big-endian and little-endian systems.^[24]

Networking[edit]

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 to be big-endian, hence the use of the term "network byte order" for big-endian byte order.^[25]

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.^[26]

The Berkeley sockets API defines a set of functions to convert 16-bit and 32-bit integers to and from network byte order: the htons (host-to-network-short) and htonl (host-to-network-long) functions convert 16-bit and 32-bit values respectively from machine (host) to network order; the ntohs and ntohl functions convert from network to host order. These functions may be a no-op on a big-endian system.

While the high-level network protocols usually consider the byte (mostly meant as octet) as their atomic unit, the lowest network protocols may deal with ordering of bits within a byte.

Bit endianness[edit]

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, HDLC, Ethernet, and USB. Some protocols use the opposite ordering (e.g. Teletext, I²C, SMBus, PMBus, and SONET and SDH^[27]). 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; the natural numbering is that the arithmetic left shift 1 << n yields a mask for the bit of position n, a rule which exhibits the machine's (byte) endianness at least if n >= 8, e.g. if used for indexing a sufficiently large bit array. Other numberings do occur in various documentations.

References[edit]

Further reading[edit]

• Danny Cohen (1980-04-01). On Holy Wars and a Plea for Peace. IETF. IEN 137. Also published at IEEE Computer, October 1981 issue.
• David V. James (June 1990). "Multiplexed buses: the endian wars continue". IEEE Micro. 10 (3): 9–21. doi:10.1109/40.56322. ISSN 0272-1732.
• Bertrand Blanc, Bob Maaraoui (December 2005). "Endianness or Where is Byte 0?" (PDF). Retrieved 2008-12-21.

External links[edit]

• Understanding big and little endian byte order
• Byte Ordering PPC
• Writing endian-independent code in C

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.