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{{About|the unit of information}}
{{Use dmy dates|date=July 2012}}
{{Fundamental info units}}

The '''bit''' (a [[portmanteau]] of '''binary digit''')<ref name="Mackenzie_1980">{{cite book |title=Coded Character Sets, History and Development |work=The Systems Programming Series |author-last=Mackenzie |author-first=Charles E. |year=1980 |edition=1 |publisher=[[Addison-Wesley Publishing Company, Inc.]] |isbn=0-201-14460-3 |lccn=77-90165 |page=x |url=https://books.google.com/books?id=6-tQAAAAMAAJ |accessdate=2016-05-22}} [https://web.archive.org/web/20160526172151/https://textfiles.meulie.net/bitsaved/Books/Mackenzie_CodedCharSets.pdf]</ref> is a [[Units of information|basic unit]] of [[information]] used in [[computing]] and digital [[communication]]s.  A binary digit can have only one of two [[value (computer science)|values]], and may be physically represented with a two-state device. These state values are most commonly represented as either a {{gaps|0|or|1}}.

The two values of a binary digit can also be interpreted as [[Truth value|logical values]] (true/false, yes/no), algebraic [[signed number|signs]] (+/&minus;), activation states (on/off), or any other two-valued attribute. The correspondence 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]]. The length of a binary number may be referred to as its [[bit-length]].

In [[information theory]], one bit is typically defined as the [[information entropy]] of a binary random variable that is 0 or 1 with equal probability,<ref>John B. Anderson, Rolf Johnnesson (2006) ''Understanding Information Transmission''.</ref> or the information that is gained when the value of such a variable becomes known.<ref>Simon Haykin (2006), ''Digital Communications''</ref><ref>[[IEEE Std 260.1-2004]]</ref>

In [[quantum computing]], a ''quantum bit'' or [[qubit]] is a [[quantum mechanics|quantum system]] that can exist in [[quantum superposition|superposition]] of two [[classical mechanics|classical]] (i.e., non-quantum) bit values.

The symbol for binary digit is either simply ''bit'' (recommended by the [[IEC 80000-13|IEC 80000-13:2008]] standard) or lowercase ''b'' (recommended by the [[IEEE 1541-2002]] and [[IEEE Std 260.1-2004]] standards). A group of eight&nbsp;binary digits is commonly called one&nbsp;[[byte]], but historically the size of the byte is not strictly defined.

As a [[unit of information]] in [[information theory]], the bit has alternatively been called a ''[[shannon (unit)|shannon]]'',<ref>{{cite web|url=https://www.unc.edu/~rowlett/units/dictB.html#bit|title=Units: B|publisher=}}</ref> named after [[Claude Shannon]], the founder of field of information theory. This usage distinguishes the quantity of information from the form of the state variables used to represent it. When the logical values are not equally probable or when a signal is not conveyed perfectly through a communication system, a binary digit in the representation of the information will convey less than one bit of information. However, the shannon unit terminology is uncommon in practice.

==History==
The encoding of data by discrete bits was used in the [[punched card]]s invented by [[Basile Bouchon]] and [[Jean-Baptiste Falcon]] (1732), developed by [[Joseph Marie Jacquard]] (1804), and later adopted by [[Semen Korsakov]], [[Charles Babbage]], [[Hermann Hollerith]], and early computer manufacturers like [[IBM]]. Another 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 [[teletype]]s and [[stock ticker machine]]s (1870).

[[Ralph Hartley]] suggested the use of a logarithmic measure of information in 1928.<ref name="abramson">Norman Abramson (1963), ''Information theory and coding''. McGraw-Hill.</ref> [[Claude E. Shannon]] first used the word '''''bit''''' in his seminal 1948 paper ''[[A Mathematical Theory of Communication]]''.<ref>{{cite journal|last=Shannon |first=Claude |title=A Mathematical Theory of Communication |journal=Bell Labs Technical Journal |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |archiveurl=https://www.webcitation.org/5s0Ome6c1?url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |archivedate=2010-08-15 }}</ref>
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". Interestingly, [[Vannevar Bush]] had written in 1936 of "bits of information" that could be stored on the [[punched card]]s used in the mechanical computers of that time.<ref>{{cite journal|last=Bush|first=Vannevar|title=Instrumental analysis|journal=Bulletin of the American Mathematical Society|year=1936|volume=42|issue=10|pages=649–669|url=http://projecteuclid.org/euclid.bams/1183499313|doi=10.1090/S0002-9904-1936-06390-1}}</ref> The first programmable computer, built by [[Konrad Zuse]], used binary notation for numbers.

==Physical representation{{anchor|representation}}==<!-- 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.

Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an [[Electricity|electrical]] [[voltage]] or [[Electric current|current]] pulse, or by the electrical state of a [[flip-flop (electronics)|flip-flop circuit]].

For devices using [[positive logic]], a digit value of 1 (or a logical value of true) is represented by a more positive voltage relative to the representation of 0. The specific voltages are different for different logic families and variations are permitted to allow for component aging and noise immunity. For example, in [[transistor–transistor logic]] (TTL) and compatible circuits, digit values 0 and 1 at the output of a device are represented by no higher than 0.4 volts and no lower than 2.6 volts, respectively; while TTL inputs are specified to recognize 0.8 volts or below as 0 and 2.2 volts or above as 1.

===Transmission and processing===
Bits are transmitted one at a time in [[serial transmission]], and by a multiple number of bits in [[parallel transmission]]. A [[bitwise operation]] optionally process bits one at a time. Data transfer rates are usually measured in decimal SI multiples of the unit [[bit per second]] (bit/s), such as kbit/s.

===Storage===
In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's [[Analytical Engine]], a bit was often stored as the position of a mechanical lever or gear, or the presence or absence of a hole at a specific point of a [[Punched card|paper card]] or [[Punched tape|tape]]. The first electrical devices for discrete logic (such as [[elevator]] and [[traffic light]] control 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|drum]]s, and [[Disk storage|disk]]s, 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]], the two values of a bit may be represented by two levels of [[electric charge]] stored in a [[capacitor]]. 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, bits are encoded as the thickness of alternating black and white lines.

==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">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.]</ref> 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.{{Quantities of bits}}

===Multiple 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. The trend in hardware design converged on the most common implementation of using eight&nbsp;bits per byte, as it is widely used today. 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)|word]]s". 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 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 1000, and the corresponding units are the [[kilobit]] (kbit) through the [[yottabit]] (Ybit).

==Information capacity and information compression==
When the information ''capacity'' of a storage system or a communication channel is presented in bits or bits per second, this often refers to binary digits, which is a [[computer hardware]] capacity to store binary code (0 or 1, up or down, current or not, etc.). Information ''capacity'' of a storage system is only an upper bound to the actual ''quantity of information'' stored therein. If the two possible values of one&nbsp;bit of storage are not equally likely, that bit of storage will contain less than one&nbsp;bit of information. Indeed, if the value is completely predictable, then the reading of that value will provide no information at all (zero entropic bits, because no resolution of uncertainty and therefore no information). If a computer file that uses ''n''&nbsp;bits of storage contains only ''m'' < ''n''&nbsp;bits of information, then that information can in principle be encoded in about ''m''&nbsp;bits, at least on the average. This principle is the basis of [[lossless data compression|data compression]] technology. Using an analogy, the hardware binary digits refer to the amount of storage space available (like the number of buckets available to store things), and the information content the filling, which comes in different levels of granularity (fine or coarse, that is, compressed or uncompressed information). When the granularity is finer (when information is more compressed), the same bucket can hold more.

For example, it is estimated that the combined technological capacity of the world to store information provides 1,300 [[exabytes]] of hardware digits in 2007. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 [[exabytes]] of information.<ref name="HilbertLopez2011">[http://www.sciencemag.org/content/332/6025/60 "The World's Technological Capacity to Store, Communicate, and Compute Information"], especially [http://www.sciencemag.org/content/suppl/2011/02/08/science.1200970.DC1/Hilbert-SOM.pdf Supporting online material], Martin Hilbert and Priscila López (2011), [[Science (journal)]], 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html</ref> 
When optimally compressed, the resulting carrying capacity approaches [[Shannon information]] or [[information entropy]].

==Bit-based computing==
Certain [[bitwise operation|bitwise]] computer [[central processing unit|processor]] instructions (such as ''bit set'') operate at the level of manipulating bits rather than manipulating data interpreted as an aggregate of bits.

In the 1980s, when [[bitmap]]ped computer displays became popular, some computers provided specialized [[bitblt|bit block transfer]] ("bitblt" or "blit") instructions to set or copy the bits that corresponded to a given rectangular area on the screen.

In most computers and programming languages, when a bit within a group of bits, such as a byte or word, is referred to, it is usually specified by a number from 0 upwards corresponding to its position within the byte or word. However, 0 can refer to either the [[most significant bit|most]] or [[least significant bit]] depending on the context.

==Other information units==
{{Main article|Units of information}}
Other units of information, sometimes used in information theory, include the ''[[natural digit]]'' also called a ''[[nat (unit)|nat]]'' or ''[[nit (unit of information)|nit]]'' and defined as [[logarithm|log]]<sub>2</sub>&nbsp;''e'' (≈ 1.443)&nbsp;bits, where ''e'' is the [[e (mathematical constant)|base of the natural logarithms]]; and the ''[[dit (unit)|dit]]'', ''[[ban (unit)|ban]]'', or ''[[hartley (unit)|hartley]]'', defined as log<sub>2</sub>&nbsp;10 (≈ 3.322)&nbsp;bits.<ref name="abramson"/> This value, slightly less than 10/3, may be understood because 10<sup>3</sup> = 1000 ≈ 1024 = 2<sup>10</sup>: three decimal digits are slightly less information than ten binary digits, so one decimal digit is slightly less than 10/3 binary digits. Conversely, one&nbsp;bit of information corresponds to about [[natural logarithm|ln]]&nbsp;2 (≈ 0.693) nats, or log<sub>10</sub>&nbsp;2 (≈ 0.301) hartleys. As with the inverse ratio, this value, approximately 3/10, but slightly more, corresponds to the fact that 2<sup>10</sup> = 1024 ~ 1000 = 10<sup>3</sup>: ten binary digits are slightly more information than three decimal digits, so one binary digit is slightly more than 3/10 decimal digits. Some authors also define a '''binit''' as an arbitrary information unit equivalent to some fixed but unspecified number of bits.<ref>{{cite book |author-first=Amitabha |author-last=Bhattacharya |title=Digital Communication |publisher=[[Tata McGraw-Hill Education]] |date=2005 |isbn=0070591172 |id={{ISBN|9780070591172}} |url=https://books.google.com/books?id=0CI8bd0upS4C&pg=PR20&lpg=PR20}}</ref>

==See also==
*[[Integer (computer science)]]
*[[Primitive data type]]
*[[Trit (computing)|Trit]] (Trinary digit)
*[[Bitstream]]
*[[Entropy (information theory)]]
*[[Baud]] (bits per second)
*[[Binary numeral system]]
*[[Ternary numeral system]]
*[[Shannon (unit)]]

==References==
{{Reflist|refs=
<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 |dead-url=no |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 |url=http://archive.computerhistory.org/resources/text/IBM/Stretch/pdfs/06-07/102632284.pdf |access-date=2016-04-04 |dead-url=no |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)|character]]s, 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}}{{cite |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 |year=1962 |chapter=4: Natural Data Units |format=PDF |pages=39–40 |url=http://archive.computerhistory.org/resources/text/IBM/Stretch/pdfs/Buchholz_102636426.pdf |access-date=2017-04-03 |dead-url=no |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 |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 |year=1959 |doi=10.1145/368424.368435}}</ref>
}}

==External links==
{{wiktionary}}
* [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] – a tool for computing file sizes, storage capacity, and digital information in various units

{{Information units}}
{{Data types}}

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