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{{short description|Unit of information}}
{{About|the unit of information}}
{{Use dmy dates|date=December 2020|cs1-dates=y}}
{{Fundamental info units}} 

The '''bit''' is the most basic [[Units of information|unit of information]] in [[computing]] and digital [[communication]]. The name is a [[portmanteau]] of '''binary digit'''.<ref name="Mackenzie_1980"/> The bit represents a [[truth value|logical state]] with one of two possible [[value (computer science)|values]]. These values are most commonly represented as either {{nowrap|"{{mono|1}}" or "{{mono|0}}"}}, but other representations such as ''true''/''false'', ''yes''/''no'', ''on''/''off'', or ''+''/''−'' are also widely used.

The relation between these values and the physical states of the underlying [[Data storage device|storage]] or [[computing device|device]] is a matter of convention, and different assignments may be used even within the same device or [[computer program|program]]. It may be physically implemented with a two-state device.

A contiguous group of binary digits is commonly called a ''[[bit string]]'', a bit vector, or a single-dimensional (or multi-dimensional) ''[[bit array]]''.
A group of eight bits is called one&nbsp;''[[byte]]'', but historically the size of the byte is not strictly defined.<ref name="Bemer_2000"/> Frequently, half, full, double and quadruple words consist of a number of bytes which is a low power of two. A string of four bits is usually a ''[[nibble]]''.

In [[information theory]], one bit is the [[information entropy]] of a random [[Binary number|binary]] variable that is 0 or 1 with equal probability,<ref name="Anderson_2006"/> or the information that is gained when the value of such a variable becomes known.<ref name="Haykin_2006"/><ref name="IEEE_260"/> As a [[unit of information]] or [[negentropy]], the bit is also known as a ''[[shannon (unit)|shannon]]'',<ref name="Rowlett"/> named after [[Claude E. Shannon]].  As a measure of the length of a digital string that is encoded as symbols over a 0-1 (binary) alphabet, the bit has been called a binit,<ref>{{cite book |last1=Breipohl |first1=Arthur M. |title=Adaptive Communication Systems |date=1963-08-18 |publisher=University of New Mexico |page=7 |url=https://digitalrepository.unm.edu/ece_etds/425/ |access-date=7 January 2025}}</ref> but this usage is now rare.<ref>{{cite web |title=binit |url=https://www.thefreedictionary.com/binit |website=The Free Dictionary |access-date=7 January 2025}}</ref>

In [[data compression]], the goal is to find a shorter representation for a string, so that it requires fewer bits during storage or transmission — but it must be "compressed" before doing so, and then "decompressed" after. The field of [[Algorithmic Information Theory]] is devoted to the study of the "irreducible information content" of a string (i.e. its shortest-possible representation length, in bits), under the assumption that the receiver has minimal ''a priori'' knowledge of the method used to compress the string. In [[error detection and correction]], the goal is to add redundant data to a string, to enable the detection and/or correction of errors during storage or transmission — but the redundant data has to be computed before doing so, and then "checked" or "corrected" after.

The symbol for the binary digit is either "bit", per the [[IEC 80000-13]]:2008 standard, or the lowercase character "b", per the [[IEEE 1541-2002]] standard. Use of the latter may create confusion with the capital "B" which is the international standard symbol for the byte.

== History ==

[[Ralph Hartley]] suggested the use of a logarithmic measure of information in 1928.<ref name="Abramson_1963"/> [[Claude E. Shannon]] first used the word "bit" in his seminal 1948 paper "[[A Mathematical Theory of Communication]]".<ref name="Shannon_1948_1"/><ref name="Shannon_1948_2"/><ref name="Shannon_1949"/> He attributed its origin to [[John W. Tukey]], who had written a Bell Labs memo on 9 January 1947 in which he contracted "binary information digit" to simply "bit".<ref name="Shannon_1948_1"/>

== Physical representation <span class="anchor" id="Representation"></span> ==
<!-- Warning: this heading is the target of a link in [[Flip-flop (electronics)]] -->
A bit can be stored by a digital device or other physical system that exists in either of two possible distinct [[state (computer science)|states]]. These may be the two stable states of a [[Flip-flop (electronics)|flip-flop]], two positions of an [[Switch|electrical switch]], two distinct [[voltage]] or [[electric current|current]] levels allowed by a [[electrical circuit|circuit]], two distinct levels of [[Irradiance|light intensity]], two directions of [[magnetism|magnetization]] or [[electrical polarity|polarization]], the orientation of reversible double stranded [[DNA]], etc.

Perhaps the earliest example of a binary storage device was the [[punched card]] invented by [[Basile Bouchon]] and Jean-Baptiste Falcon (1732), developed by [[Joseph Marie Jacquard]] (1804), and later adopted by [[Semyon Korsakov]], [[Charles Babbage]], [[Herman Hollerith]], and early computer manufacturers like [[IBM]]. A variant of that idea was the perforated [[paper tape]]. In all those systems, the medium (card or tape) conceptually carried an array of hole positions; each position could be either punched through or not, thus carrying one&nbsp;bit of information. The encoding of text by bits was also used in [[Morse code]] (1844) and early digital communications machines such as [[Teleprinter|teletypes]] and [[stock ticker machine]]s (1870).

The first electrical devices for discrete logic (such as [[elevator]] and [[traffic light]] control [[Electronic circuit|circuits]], [[telephone switches]], and Konrad Zuse's computer) represented bits as the states of [[electrical relay]]s which could be either "open" or "closed". When relays were replaced by [[vacuum tube]]s, starting in the 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a [[mercury delay line]], charges stored on the inside surface of a [[cathode-ray tube]], or opaque spots printed on [[optical disc|glass discs]] by [[photolithographic]] techniques.

In the 1950s and 1960s, these methods were largely supplanted by [[magnetic storage]] devices such as [[magnetic-core memory]], [[magnetic tape]]s, [[magnetic drum|drums]], and [[Disk storage|disks]], where a bit was represented by the polarity of [[magnetism|magnetization]] of a certain area of a [[ferromagnetic]] film, or by a change in polarity from one direction to the other. The same principle was later used in the [[magnetic bubble memory]] developed in the 1980s, and is still found in various [[magnetic strip]] items such as [[Rapid transit|metro]] tickets and some [[credit card]]s.

In modern [[semiconductor memory]], such as [[dynamic random-access memory]] or a [[solid-state drive]], the two values of a bit are represented by two levels of [[electric charge]] stored in a [[capacitor]] or a [[floating-gate MOSFET]]. In certain types of [[programmable logic array]]s and [[read-only memory]], a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In [[optical disc]]s, a bit is encoded as the presence or absence of a [[microscopic]] pit on a reflective surface. In one-dimensional [[bar code]]s and two-dimensional [[QR codes]], bits are encoded as lines or squares which may be either black or white.

In modern digital computing, bits are transformed in Boolean [[logic gate]]s.

=== Transmission and processing ===
Bits are transmitted one at a time in [[serial transmission]]. By contrast, multiple bits are transmitted simultaneously in a [[parallel transmission]]. A [[serial computer]] processes information in either a bit-serial or a byte-serial fashion.  From the standpoint of data communications, a byte-serial transmission is an 8-way parallel transmission with binary signalling.

In programming languages such as [[C (programming language) |C]], a [[bitwise operation]] operates on binary strings as though they are vectors of bits, rather than interpreting them as [[binary number]]s.

Data transfer rates are usually measured in decimal SI multiples.  For example, a [[channel capacity]] may be specified as 8 kbit/s = 8 kb/s = 1 kB/s.

=== Storage ===

File sizes are often measured in (binary) IEC multiples of bytes, for example 1 KiB = 1024 bytes = 8192 bits.  Confusion may arise in cases where (for historic reasons) filesizes are specified with binary multipliers using the ambiguous prefixes K, M, and G rather than the IEC standard prefixes Ki, Mi, and Gi.<ref>{{cite web |title=UnitsPolicy - Ubuntu Wiki |url=https://wiki.ubuntu.com/UnitsPolicy |access-date=7 January 2025}}</ref>

Mass storage devices are usually measured in decimal SI multiples, for example 1 TB = <math>10^{12}</math> bytes.  

Confusingly, the storage capacity of a directly-addressable memory device, such as a [[Dynamic Random Access Memory |DRAM]] chip, or an assemblage of such chips on a memory module, is specified as a binary multiple -- using the ambiguous prefix G rather than the IEC recommended Gi prefix.  For example, a DRAM chip that is specified (and advertised) as having "1 GB" of capacity has <math>2^{30}</math> bytes of capacity.  As at 2022, the difference between the popular understanding of a memory system with "8 GB" of capacity, and the SI-correct meaning of "8 GB" was still causing difficulty to software designers.<ref>{{cite web |title=Use MB/GB/TB suffix for VM memory input |url=https://github.com/netbox-community/netbox/issues/8437 |website=Github Netbox Community |access-date=8 January 2025 |date=2022}}</ref>

== Unit and symbol ==
The bit is not defined in the [[International System of Units]] (SI). However, the [[International Electrotechnical Commission]] issued standard [[IEC 60027]], which specifies that the symbol for binary digit should be 'bit', and this should be used in all multiples, such as 'kbit', for kilobit.<ref name="NIST_2008"/> However, the lower-case letter 'b' is widely used as well and was recommended by the [[IEEE 1541-2002|IEEE 1541 Standard (2002)]]. In contrast, the upper case letter 'B' is the standard and customary symbol for byte.

=== Multiple bits ===
{{redirect|MBit|the technical high school|MBIT}}
{{Quantities of bits}}
Multiple bits may be expressed and represented in several ways. For convenience of representing commonly reoccurring groups of bits in information technology, several [[units of information]] have traditionally been used. The most common is the unit [[byte]], coined by [[Werner Buchholz]] in June 1956, which historically was used to represent the group of bits used to encode a single [[character (computing)|character]] of text (until [[UTF-8]] multibyte encoding took over) in a computer<ref name="Bemer_2000"/><ref name="Buchholz_1956"/><ref name="Buchholz_1977"/><ref name="Buchholz_1962"/><ref name="Bemer_1959"/> and for this reason it was used as the basic [[address space|addressable]] element in many [[computer architecture]]s. By 1993, the trend in hardware design had converged on the 8-bit [[byte]].<ref>{{cite web |title=ISO/IEC 2382-1:1993(en) Information technology — Vocabulary — Part 1: Fundamental terms |url=https://www.iso.org/obp/ui/#iso:std:iso-iec:2382:-1:ed-3:v1:en |access-date=8 January 2025 |page=01.02.09}}</ref>  However, because of the ambiguity of relying on the underlying hardware design, the unit [[Octet (computing)|octet]] was defined to explicitly denote a sequence of eight&nbsp;bits.

Computers usually manipulate bits in groups of a fixed size, conventionally named "[[Word (computer architecture)|words]]". Like the byte, the number of bits in a word also varies with the hardware design, and is typically between 8 and 80&nbsp;bits, or even more in some specialized computers. In the early 21st century, retail personal or server computers have a word size of 32 or 64&nbsp;bits.

The [[International System of Units]] defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes [[kilo-|kilo]] (10<sup>3</sup>) through [[yotta-|yotta]] (10<sup>24</sup>) increment by multiples of one thousand, and the corresponding units are the [[kilobit]] (kbit) through the [[yottabit]] (Ybit).

== See also ==
* {{Annotated link|Baud}}
* {{Annotated link|Binary numeral system}}
* {{Annotated link|Bit rate}}
* {{Annotated link|Bitstream}}
* {{Annotated link|Entropy (information theory)}}
* {{Annotated link|Fuzzy bit}}
* {{Annotated link|Integer (computer science)}}
* {{Annotated link|Primitive data type}}
* {{Annotated link|Qubit}} (quantum bit)
* {{Annotated link|Shannon (unit)}}
* {{Annotated link|Ternary numeral system}}
* {{Annotated link|Trit (computing)}} (Trinary digit)

== References ==
{{reflist|refs=
<ref name="Mackenzie_1980">{{cite book |url=https://textfiles.meulie.net/bitsaved/Books/Mackenzie_CodedCharSets.pdf |title=Coded Character Sets, History and Development |series=The Systems Programming Series |author-last=Mackenzie |author-first=Charles E. |date=1980 |edition=1 |publisher=[[Addison-Wesley Publishing Company, Inc.]] |isbn=978-0-201-14460-4 |lccn=77-90165 |page=x |access-date=2019-08-25 |archive-url=https://web.archive.org/web/20160526172151/https://textfiles.meulie.net/bitsaved/Books/Mackenzie_CodedCharSets.pdf |archive-date=May 26, 2016 |url-status=live |df=mdy-all }}</ref>
<ref name="Anderson_2006">{{citation |author-first1=John B. |author-last1=Anderson |author-first2=Rolf |author-last2=Johnnesson |date=2006 |title=Understanding Information Transmission}}</ref>
<ref name="Haykin_2006">{{citation |author-first=Simon |author-last=Haykin |date=2006 |title=Digital Communications}}</ref>
<ref name="IEEE_260">[[IEEE Std 260.1-2004]]</ref>
<ref name="Rowlett">{{cite web |url=https://www.unc.edu/~rowlett/units/dictB.html#bit |title=Units: B |url-status=live |archive-url=https://web.archive.org/web/20160504055432/http://www.unc.edu/~rowlett/units/dictB.html#bit |archive-date=2016-05-04}}</ref>
<ref name="Abramson_1963">{{cite book |author-first=Norman |author-last=Abramson |date=1963 |title=Information theory and coding |publisher=[[McGraw-Hill]]}}</ref>
<ref name="NIST_2008">National Institute of Standards and Technology (2008), ''Guide for the Use of the International System of Units''. [http://physics.nist.gov/cuu/pdf/sp811.pdf Online version.] {{webarchive|url=https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf |date=3 June 2016}}</ref>
<!-- UNUSED REF <ref name="Bush_1936">{{cite journal |author-last=Bush |author-first=Vannevar |author-link=Vannevar Bush |title=Instrumental analysis |journal=[[Bulletin of the American Mathematical Society]] |date=1936 |volume=42 |issue=10 |pages=649–669 |url=http://projecteuclid.org/euclid.bams/1183499313 |doi=10.1090/S0002-9904-1936-06390-1 |url-status=live |archive-url=https://web.archive.org/web/20141006153002/http://projecteuclid.org/euclid.bams/1183499313 |archive-date=2014-10-06|doi-access=free }}</ref> -->
<ref name="Shannon_1948_1">{{cite journal |author-last=Shannon |author-first=Claude Elwood |author-link=Claude Elwood Shannon |title=A Mathematical Theory of Communication |journal=[[Bell System Technical Journal]] |volume=27 |issue=3 |pages=379–423 |date=July 1948 |doi=10.1002/j.1538-7305.1948.tb01338.x |hdl=11858/00-001M-0000-002C-4314-2 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |via=Bell Labs Computing and Mathematical Sciences Research |archive-url=https://web.archive.org/web/19980715013250/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |url-status=dead |archive-date=1998-07-15 |quote=The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly ''bits'', a word suggested by [[John Wilder Tukey|J. W. Tukey]].|hdl-access=free }}</ref>
<ref name="Shannon_1948_2">{{cite journal |author-last=Shannon |author-first=Claude Elwood |author-link=Claude Elwood Shannon |title=A Mathematical Theory of Communication |journal=[[Bell System Technical Journal]] |volume=27 |issue=4 |pages=623–666 |date=October 1948 |doi=10.1002/j.1538-7305.1948.tb00917.x |hdl=11858/00-001M-0000-002C-4314-2|hdl-access=free }}</ref>
<ref name="Shannon_1949">{{cite book |author-last1=Shannon |author-first1=Claude Elwood |author-link1=Claude Elwood Shannon |author-first2=Warren |author-last2=Weaver |author-link2=Warren Weaver |title=A Mathematical Theory of Communication |publisher=[[University of Illinois Press]] |date=1949 |isbn=0-252-72548-4 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |via=Bell Labs Computing and Mathematical Sciences Research |archive-url=https://web.archive.org/web/19980715013250/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |url-status=dead |archive-date=1998-07-15}}</ref>
<ref name="Bemer_2000">{{cite web |title=Why is a byte 8 bits? Or is it? |author-first=Robert William |author-last=Bemer |author-link=Robert William Bemer |date=2000-08-08 |work=Computer History Vignettes |url=http://www.bobbemer.com/BYTE.HTM |access-date=2017-04-03 |url-status=dead |archive-url=https://web.archive.org/web/20170403130829/http://www.bobbemer.com/BYTE.HTM |archive-date=2017-04-03 |quote=[…] With [[IBM]]'s [[IBM STRETCH|STRETCH]] computer as background, handling 64-character words divisible into groups of 8 (I designed the character set for it, under the guidance of Dr. [[Werner Buchholz]], the man who DID coin the term "[[byte]]" for an 8-bit grouping). […] The [[IBM System 360|IBM 360]] used 8-bit characters, although not ASCII directly. Thus Buchholz's "byte" caught on everywhere. I myself did not like the name for many reasons. […]}}</ref>
<ref name="Buchholz_1956">{{cite book |title=The Link System |chapter=7. The Shift Matrix |author-first=Werner |author-last=Buchholz |author-link=Werner Buchholz |date=1956-06-11 |id=[[IBM Stretch|Stretch]] Memo No. 39G |publisher=[[IBM]] |pages=5–6 |chapter-url=http://archive.computerhistory.org/resources/text/IBM/Stretch/pdfs/06-07/102632284.pdf |access-date=2016-04-04 |url-status=live |archive-url=https://web.archive.org/web/20170404152534/http://archive.computerhistory.org/resources/text/IBM/Stretch/pdfs/06-07/102632284.pdf |archive-date=2017-04-04 |quote=[…] Most important, from the point of view of editing, will be the ability to handle any characters or digits, from 1 to 6 bits long […] the Shift Matrix to be used to convert a 60-bit [[word (computer architecture)|word]], coming from Memory in parallel, into [[character (computing)|characters]], or "[[byte]]s" as we have called them, to be sent to the [[serial adder|Adder]] serially. The 60 bits are dumped into [[magnetic core]]s on six different levels. Thus, if a 1 comes out of position 9, it appears in all six cores underneath. […] The Adder may accept all or only some of the bits. […] Assume that it is desired to operate on 4 bit [[decimal digit]]s, starting at the right. The 0-diagonal is pulsed first, sending out the six bits 0 to 5, of which the Adder accepts only the first four (0-3). Bits 4 and 5 are ignored. Next, the 4 diagonal is pulsed. This sends out bits 4 to 9, of which the last two are again ignored, and so on. […] It is just as easy to use all six bits in [[alphanumeric]] work, or to handle bytes of only one bit for logical analysis, or to offset the bytes by any number of bits. […]}}</ref>
<ref name="Buchholz_1977">{{cite journal |author-last=Buchholz |author-first=Werner |author-link=Werner Buchholz |title=The Word "Byte" Comes of Age... |journal=[[Byte Magazine]] |date=February 1977 |volume=2 |issue=2 |page=144 |url=https://archive.org/stream/byte-magazine-1977-02/1977_02_BYTE_02-02_Usable_Systems#page/n145/mode/2up |quote=[…] The first reference found in the files was contained in an internal memo written in June 1956 during the early days of developing [[IBM Stretch|Stretch]]. A [[byte]] was described as consisting of any number of parallel bits from one to six. Thus a byte was assumed to have a length appropriate for the occasion. Its first use was in the context of the input-output equipment of the 1950s, which handled six bits at a time. The possibility of going to 8 bit bytes was considered in August 1956 and incorporated in the design of Stretch shortly thereafter. The first published reference to the term occurred in 1959 in a paper "Processing Data in Bits and Pieces" by [[Gerrit Anne Blaauw|G&nbsp;A&nbsp;Blaauw]], [[Frederick Phillips Brooks, Jr.|F&nbsp;P&nbsp;Brooks&nbsp;Jr]] and [[Werner Buchholz|W&nbsp;Buchholz]] in the ''[[IRE Transactions on Electronic Computers]]'', June 1959, page 121. The notions of that paper were elaborated in Chapter 4 of ''[[#Buchholz-1962|Planning a Computer System (Project Stretch)]]'', edited by W&nbsp;Buchholz, [[McGraw-Hill Book Company]] (1962). The rationale for coining the term was explained there on page 40 as follows:<br />Byte ''denotes a group of bits used to encode a character, or the number of bits transmitted in parallel to and from input-output units. A term other than ''character'' is used here because a given character may be represented in different applications by more than one code, and different codes may use different numbers of bits (ie, different byte sizes). In input-output transmission the grouping of bits may be completely arbitrary and have no relation to actual characters. (The term is coined from ''[[bite]]'', but respelled to avoid accidental mutation to ''bit''.)''<br />[[System/360]] took over many of the Stretch concepts, including the basic byte and word sizes, which are powers of 2. For economy, however, the byte size was fixed at the 8 bit maximum, and addressing at the bit level was replaced by byte addressing. […]}}</ref>
<ref name="Buchholz_1962">{{anchor|Buchholz-1962}}{{citation |title=Planning a Computer System – Project Stretch |author-first1=Gerrit Anne |author-last1=Blaauw |author-link1=Gerrit Anne Blaauw |author-first2=Frederick Phillips |author-last2=Brooks, Jr. |author-link2=Frederick Phillips Brooks, Jr. |author-first3=Werner |author-last3=Buchholz |author-link3=Werner Buchholz |editor-first=Werner |editor-last=Buchholz |editor-link=Werner Buchholz |publisher=[[McGraw-Hill Book Company, Inc.]] / The Maple Press Company, York, PA. |lccn=61-10466 |date=1962 |chapter=Chapter 4: Natural Data Units |pages=39–40 |chapter-url=http://archive.computerhistory.org/resources/text/IBM/Stretch/pdfs/Buchholz_102636426.pdf |access-date=2017-04-03 |url-status=dead |archive-url=https://web.archive.org/web/20170403014651/http://archive.computerhistory.org/resources/text/IBM/Stretch/pdfs/Buchholz_102636426.pdf |archive-date=2017-04-03}}</ref>
<ref name="Bemer_1959">{{cite journal |author-first=Robert William |author-last=Bemer |author-link=Robert William Bemer |title=A proposal for a generalized card code of 256 characters |journal=[[Communications of the ACM]] |volume=2 |number=9 |pages=19–23 |date=1959 |doi=10.1145/368424.368435|s2cid=36115735 |doi-access=free }}</ref>
}}

== External links ==
{{wiktionary}}
* [https://web.archive.org/web/20090216151053/http://www.bit-calculator.com/ Bit Calculator] – a tool providing conversions between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte
* [http://nxu.biz/tools/BitXByteConverter/ BitXByteConverter] {{Webarchive|url=https://web.archive.org/web/20160406223558/http://nxu.biz/tools/BitXByteConverter/ |date=2016-04-06 }} – a tool for computing file sizes, storage capacity, and digital information in various units

{{Information units}}
{{Data types}}
{{Authority control}}

[[Category:Binary arithmetic]]
[[Category:Primitive types]]
[[Category:Data types]]
[[Category:Units of information]]