Endianness
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In computing, endianness is the ordering used to represent some kind of data as a sequence of smaller units. Typical cases are the order in which integer values are stored as bytes in computer memory (relative to a given memory addressing scheme) and the transmission order over a network or other medium. When specifically talking about bytes, endianness is also referred to simply as byte order.[1]
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[edit] Endianness as a general concept
Generally speaking, endianness is a particular facet of a representation format. As such, it applies to the representation(s) of integers used by computer processors, to encoding schemes such as UTF-16 and UTF-32 or to the conceptual encoding implied by some low-level algorithms (see for instance MD5 and SHA hash functions). Likewise it applies to network transmissions, where it is established by the employed protocol.
A note on some non-idiomatic usages: some authors extend the usage of the word "endianness", and of related terms, to entities such as street addresses, date formats and others. It should be noticed however that such usages —basically reducing endianness to a mere synonym of ordering of the parts— are non-standard usage (e.g., ISO 8601:2004 talks about "descending order year-month-day", not about "big-endian format"), do not have widespread usage, and are generally (other than for date formats) employed in a metaphorical sense.
[edit] Endianness and hardware
Most computer processors simply store integers as sequences of bytes, so that, conceptually, the encoded value can be obtained by simple concatenation. For an n-byte integer value this allows n! (n factorial) possible representations (one for each byte permutation). The two most common of them are
- increasing numeric significance with increasing memory addresses, known as little-endian, and
- its opposite, called big-endian.[2]
x86 processors use the little-endian format (sometimes called the Intel format).
Motorola processors have generally used big-endian. PowerPC (which includes Apple's Macintosh line prior to the Intel switch) and System/370 also adopt big-endian. SPARC historically used big-endian, though version 9 is bi-endian (see below).
[edit] Bi-endian hardware
Some architectures —including ARM, PowerPC (but not the PPC970/G5), DEC Alpha, SPARC V9, MIPS, PA-RISC and IA64— feature switchable endianness. That can improve performance or simplify the logic of networking devices and software. The word bi-endian, said of hardware, denotes the capability to compute or pass data in either of two different endian formats (usually big-endian and little-endian).
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 DEC Alpha, which runs only in big-endian mode on the Cray T3E).
Note that "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.
Note, too, that some nominally bi-endian CPUs may actually employ internal "magic" (as opposed to really switching to a different endianness) in one of their operating modes. For instance, some PowerPC processors in little-endian mode act as little-endian from the point of view of the executing programs but they do not actually store data in memory in little-endian format (multi-byte values are swapped during memory load/store operations). This can cause problems when memory is transferred to an external device if some part of the software, e.g. a device driver, does not account for the situation.
[edit] Discussion, background, etymology
The choice of big-endian vs. little endian has been the subject of flame wars. The very term big-endian comes from Jonathan Swift's satiric novel Gulliver’s Travels, where tensions are described in Lilliput and Blefuscu because a faction called the Big-endians prefer to crack open their soft-boiled eggs from the big end, contrary to Lilliputian royal edict.[3] The terms little-endian and endianness have a similar ironic intent.[4]
An often cited argument in favour of big-endian is that it is consistent with the ordering used in natural languages. But that is far from being universal, both in spoken and written form:
- spoken: though most spoken languages express most numbers, especially those larger than a hundred, in a "big-endian manner"[5] (in modern English, for example, one says "twenty-four", not "four-and-twenty") there are notable exceptions such as the German, Danish, and the Dutch languages, which use "little-endian" for numbers up to 99 and "mixed endianness" for larger numbers (e.g. vierundzwanzig/vierentwintig (24, literally "four-and-twenty"), and hundertvierundzwanzig (124, literally "hundred four-and-twenty"). Sanskrit language is a larger exception which uses "little-endian" for small (e.g. chaturvinsh (24, literally "four-and-twenty")) as well as large numbers (e.g. chaturvinshatyadhikashatatam (124, literally "four-and-twenty-over-hundred")).
- written: the Hindu-Arabic numeral system is used worldwide and is such that the most significant digits are always written to the left of the less significant ones. Writing left to right, this system is therefore "big-endian". Writing right to left, this numeral system is "little-endian". It is worth noting, also, that in quite a few languages the spoken order of numerals is inconsistent with how they appear written; and that in some languages, such as Persian and Hebrew, it is common to interrupt the writing of text (right-to-left) to write a number in the opposite order (left-to-right)
Little-endian has the property that, in the absence of alignment restrictions, values can be read from memory at different widths without using different addresses. 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), or 32-bit (0000004A). (This example works only if the value makes sense in all three sizes, which means the value fits in just 8 bits.) This little-endian property is rarely used, and doesn't imply that little-endian has any performance advantage in variable-width data access.
[edit] Examples of storing the value 0x0A0B0C0D in memory
- Note: the prefix 0x indicates hexadecimal notation.
To further illustrate the above notions this section provides example layouts of a 32-bit number in the most common variants of endianness. There is no general guarantee that a platform will use one of these formats but in practice there are few if any exceptions.
All the examples refer to the storage in memory of the value 0x0A0B0C0D.
[edit] Big-endian
- With 8-bit atomic element size and 1-byte (octet) address increment:
| increasing addresses → | |||||
| 0x0A | 0x0B | 0x0C | 0x0D | ||
The most significant byte (MSB) value, which is 0x0A in our example, is stored at the memory location with the lowest address, the next byte value in significance, 0x0B, is stored at the following memory location and so on. This is akin to Left-to-Right reading order in hexadecimal.
- With 16-bit atomic element size:
| increasing addresses → | |||||
| 0x0A0B | 0x0C0D | ||||
The most significant atomic element stores now the value 0x0A0B, followed by 0x0C0D.
[edit] Little-endian
- With 8-bit atomic element size and 1-byte (octet) address increment:
| increasing addresses → | |||||
| 0x0D | 0x0C | 0x0B | 0x0A | ||
The least significant byte (LSB) value, 0x0D, is at the lowest address. The other bytes follow in increasing order of significance.
- With 16-bit atomic element size:
| increasing addresses → | |||||
| 0x0C0D | 0x0A0B | ||||
The least significant 16-bit unit stores the value 0x0C0D, immediately followed by 0x0A0B.
[edit] Middle-endian
Still other architectures, generically called middle-endian or mixed-endian, may have a more complicated ordering; PDP-11, for instance, stored some 32-bit words, counting from the most significant, as: 2nd byte first, then 1st, then 4th, and finally 3rd.
- storage of a 32-bit word on a PDP-11
| increasing addresses → | |||||
| 0x0B | 0x0A | 0x0D | 0x0C | ||
Note that this can be interpreted as storing the most significant "half" (16-bits) followed by the less significant half (as if big-endian) but with each half stored in little-endian format. This ordering is known as PDP-endianness.
[edit] Endianness in networking
Networks generally use big-endian order; the historical reason is that this allowed routing while a telephone number was being composed. In fact, the Internet Protocol defines a standard big-endian network byte order. This byte order is used for all numeric values in the packet headers and by many higher level protocols and file formats that are designed for use over IP. The Berkeley sockets API defines a set of functions to convert 16- and 32-bit integers to and from network byte order: the htonl (host-to-network-long) and htons (host-to-network-short) functions convert 32-bit and 16-bit values respectively from machine (host) to network order; whereas the ntohl and ntohs functions convert from network to host order.
While the lowest network protocols may deal with sub-byte formatting, all the layers above them usually consider the byte (mostly meant as octet) as their atomic unit.
[edit] "Bit endianness"
The terms bit endianness or bit-level endianness are seldom used when talking about the representation of a stored value, as they are only meaningful for the rare computer architectures which support addressing of individual bits. They are used however to refer to the transmission order of bits over a serial medium. Most often that order is transparently managed by the hardware and is the bit-level analogue of little-endian (low-bit first), although protocols exist which require the opposite ordering (e.g. I²C). In networking, the decision about the order of transmission of bits is made in the very bottom of the data link layer of the OSI model.
[edit] Notes
- ^ For hardware, the Jargon File also reports the less common expression byte sex [1]. It is unclear whether this terminology is also used when more than two orderings are possible. Similarly, the manual for the ORCA/M assembler refers to a field indicating the order of the bytes in a number field as
NUMSEX. - ^ Note that, in these expressions, the term "end" is meant as "extremity", not as "last part"; and that big and little say which extremity is written first.
- ^ Gulliver's Travels (Part I, Chapter IV) on Wikisource
- ^ Endian FAQ – includes the paper Internet Engineering Note (IEN) 137: On Holy Wars and a Plea for Peace ftp mirror by Danny Cohen (1 April 1980), but adds much more context.
- ^ Cf. entries 539 and 704 of the Linguistic Universals Database
[edit] External links
- White Paper: Endianness or Where is Byte 0?
This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.
