Big endian

When integers or any other data are represented with multiple bytes, the actual ordering of those bytes in memory, or the sequence in which they are transmitted over some medium, is subject to convention.

This is similar to the situation in written languages, where some are written left-to-right, while others are written right-to-left. The convention is called endianness, describing the method either big-endian or little-endian. Endianness is also referred to as byte sex. Note that the endianness does not matter in dealing with a sequence of single bytes. This is the case of a single-byte string literal where one byte corresponds to one character. Strings encoded with unicode UTF-16 or UTF-32 are affected by endianness because in those, a set of two or four bytes represents one character.

Endianness in computers

When some computers store a 32-bit integer value in memory, for example 0xA0B70708 (in hexadecimal notation), they store it as bytes in the following order: A0 B7 07 08. That is, the most significant byte (A0 in our example) is stored at the memory location with the lowest address, the next significant byte B7 is stored at the next memory location and so on.

Architectures that follow this rule are called big-endian and include Motorola 68000, SPARC and System/370.

Other computers store 0xA0B70708 as 08 07 B7 A0, that is, least significant byte first. Architectures that follow this rule are called little-endian and include the MOS Technology 6502, Intel x86 and DEC VAX.

Some architectures can be configured either way; these include ARM, PowerPC, DEC Alpha, MIPS and IA64. The word bytesexual, said of hardware, denotes willingness to compute or pass data in either big-endian or little-endian format (depending, presumably, on a mode bit somewhere).

Still other (generally older) architectures, called middle-endian, may have a more complicated ordering such that the bytes within a 16-bit unit are ordered differently from the 16-bit units within a 32-bit word. For instance, 07 08 A0 B7. Middle-endian architectures include the PDP family of processors. In general, inconsistent endianness is more confusing to work with than consistent big- or little-endianness.

Endianness also applies in the numbering of the bits within a byte or word. In a consistently big-endian architecture the bits in the word are numbered from the left, bit zero being the most significant bit and bit 7 being the least significant bit in a byte. The favored endianness depends somewhat on where the computer users expect the binary point to be located in a number. It seems most intuitive to number the bits in the little-endian order if the byte is taken to represent an integer. In this case the bit number corresponds to the exponent of the numeric weight of the bit. However, if the byte is taken to represent a binary fraction, with the binary point to the left of the most significant bit, then the big-endian numbering convention is more convenient. When computers are actually used for numerical computation, numbers are usually represented as scaled binary fractions.

Endianness in communications

In general, the NUXI problem is the problem of transferring data between computers with differing byte order. For example, the string "UNIX", packed two bytes per 16-bit word integer, might look like "NUXI" on a machine with a different "byte sex". The problem is caused by the difference in endianness. The problem was first discovered when porting an early version of Unix from PDP-11 (a little-endian architecture) to a big-endian IBM architecture.

The Internet Protocol defines a standard "big-endian" network byte order, where binary values are in general encoded into packets, and sent out over the network, most significant byte first. This occurs regardless of the native endianness of the host CPU.

Serial devices also have bit-endianness: the bits in a byte can be sent little-endian (least significant bit first) or big-endian (most significant bit first). This decision is made in the very bottom of the data link layer of the OSI model.

Endianness, software, and portability

Endianness has implications in software portability. For example, in interpreting data stored in binary format and using an appropriate bitmask, the endianness is important because different endianness will lead to different results from the mask.

Writing binary data from software to a common format leads to a concern of the proper endianness. For example saving data in the BMP bitmap format requires little endian integers - if the data are stored using big endian integers then the data will be corrupted since they do not match the format.

The OPENSTEP operating system has software that swaps the bytes of integers and other C datatypes in order to preserve the correct endianness, since software running on OPENSTEP for PA-RISC is intended to be portable to OPENSTEP running on Mach/i386.

Discussion, background

Big-endian numbers are easier to read when debugging a program but less intuitive (because the high byte is at the smaller address); conversely, little-endian numbers are more intuitive but harder to debug. The choice of big-endian vs. little-endian for a CPU design has begun a lot of flame wars. Emphasizing the futility of this argument, the very terms big-endian and little-endian were taken from the Big-Endians and Little-Endians of Jonathan Swift's novel Gulliver's Travels, two peoples in conflict over which end to crack an egg in the voyage to Lilliput and Blefuscu.

See the Endian FAQ (external link, below), including the significant essay "On Holy Wars and a Plea for Peace" by Danny Cohen (1980).

The written system of arabic numerals is used world-wide and is such that the most significant digits are always written to the left of the less significant ones. In languages that write text left-to-right, this system is therefore big-endian, in languages that write right-to-left, this numeral system is little-endian. The spoken numeral system in English is big endian (with minor exceptions: we say "seventeen" instead of "ten-seven"). German, as well as Dutch, uses a strange mixture of big- and little-endianness: 376 is pronounced as "Dreihundertsechsundsiebzig", i.e. "three hundred six-and-seventy".

Spelling

There seems to be quite some confusion about how endianness is spelled. The two popular variants are endianness (34800 hits in Google) and endianess (12600 hits). There are even 900 Webpages containing both variants. Neither of the two variants appear in current dictionaries, so it is hard to tell which variant is correct. It seems, however, that endianness is generally more accepted and it is also used in this page.

References