Misplaced Pages

Bit: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editContent deleted Content addedVisualWikitext
Revision as of 07:35, 8 November 2024 editEEng (talk | contribs)Edit filter helpers, Autopatrolled, Extended confirmed users, New page reviewers, Pending changes reviewers, Template editors97,947 edits (dummy edit) Prior edit summary should have read: "The emphasis on this distinction appears to be an idiosyncratic idea of the editor adding it here, who BTW wrote the cited paper. If this is worth mentioning, there ought to be standard references (IEEE?) giving prominence to the distinction"← Previous edit Latest revision as of 05:46, 8 January 2025 edit undoCthombor (talk | contribs)224 edits →Storage: Discussing the two meanings of "GB" arising commonly in specifications of disk drives and DRAM memory modules 
(47 intermediate revisions by 15 users not shown)
Line 1: Line 1:
{{short description|Unit of information}} {{short description|Unit of information}}
{{About|the unit of information}} {{About|the unit of information}}
{{Redir|Qbit (quettabit)|quantum bits|Qubit}}
{{Use dmy dates|date=December 2020|cs1-dates=y}} {{Use dmy dates|date=December 2020|cs1-dates=y}}
{{Fundamental info units}} {{Fundamental info units}}
Line 12: Line 11:
A group of eight bits is called one&nbsp;'']'', 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 '']''. A group of eight bits is called one&nbsp;'']'', 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 '']''.


In ], one bit is the ] of a random ] 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 ], the bit is also known as a '']'',<ref name="Rowlett"/> named after ]. In ], one bit is the ] of a random ] 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 ] or ], the bit is also known as a '']'',<ref name="Rowlett"/> named after ]. 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 ], the goal is to find a shorter representation for a string, so that it requires fewer bits of storage -- but it must be "compressed" before storage and then (generally) "decompressed" before it is used in a computation. The field of ] 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.


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


== History == == History ==
⚫ The encoding of data by discrete bits was used in the ]s invented by ] and Jean-Baptiste Falcon (1732), developed by ] (1804), and later adopted by ], ], ], and early computer manufacturers like ]. A variant of that idea was the perforated ]. 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 ] (1844) and early digital communications machines such as ] and ]s (1870).


] suggested the use of a logarithmic measure of information in 1928.<ref name="Abramson_1963"/> ] first used the word "bit" in his seminal 1948 paper "]".<ref name="Shannon_1948_1"/><ref name="Shannon_1948_2"/><ref name="Shannon_1949"/> He attributed its origin to ], 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"/> ] suggested the use of a logarithmic measure of information in 1928.<ref name="Abramson_1963"/> ] first used the word "bit" in his seminal 1948 paper "]".<ref name="Shannon_1948_1"/><ref name="Shannon_1948_2"/><ref name="Shannon_1949"/> He attributed its origin to ], 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"/>
Line 25: Line 25:
A bit can be stored by a digital device or other physical system that exists in either of two possible distinct ]. These may be the two stable states of a ], two positions of an ], two distinct ] or ] levels allowed by a ], two distinct levels of ], two directions of ] or ], the orientation of reversible double stranded ], etc. A bit can be stored by a digital device or other physical system that exists in either of two possible distinct ]. These may be the two stable states of a ], two positions of an ], two distinct ] or ] levels allowed by a ], two distinct levels of ], two directions of ] or ], the orientation of reversible double stranded ], etc.


⚫ Perhaps the earliest example of a binary storage device was the ] invented by ] and Jean-Baptiste Falcon (1732), developed by ] (1804), and later adopted by ], ], ], and early computer manufacturers like ]. A variant of that idea was the perforated ]. 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 ] (1844) and early digital communications machines such as ] and ]s (1870).
Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an ] ] or ] pulse, or by the electrical state of a flip-flop circuit.


⚫ The first electrical devices for discrete logic (such as ] and ] control ], ], and Konrad Zuse's computer) represented bits as the states of ]s which could be either "open" or "closed". When relays were replaced by ]s, starting in the 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a ], charges stored on the inside surface of a ], or opaque spots printed on ] by ] techniques.
For devices using ], a digit value of {{mono|1}} (or a logical value of true) is represented by a more positive voltage relative to the representation of {{mono|0}}. Different logic families require different voltages, and variations are allowed to account for component aging and noise immunity. For example, in ] (TTL) and compatible circuits, digit values {{mono|0}} and {{mono|1}} at the output of a device are represented by no higher than 0.4&nbsp;V and no lower than 2.6&nbsp;V, respectively; while TTL inputs are specified to recognize 0.8&nbsp;V or below as {{mono|0}} and 2.2&nbsp;V or above as {{mono|1}}.

⚫ In the 1950s and 1960s, these methods were largely supplanted by ] devices such as ], ]s, ], and ], where a bit was represented by the polarity of ] of a certain area of a ] film, or by a change in polarity from one direction to the other. The same principle was later used in the ] developed in the 1980s, and is still found in various ] items such as ] tickets and some ]s.

⚫ In modern ], such as ] or a ], the two values of a bit are represented by two levels of ] stored in a ] or a ]. In certain types of ]s and ], a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In ]s, a bit is encoded as the presence or absence of a ] pit on a reflective surface. In one-dimensional ]s and two-dimensional ], bits are encoded as lines or squares which may be either black or white.

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


=== Transmission and processing === === Transmission and processing ===
Bits are transmitted one at a time in ], and by a multiple number of bits in ]. A ] optionally processes bits one at a time. Data transfer rates are usually measured in decimal SI multiples of the unit ] (bit/s), such as kbit/s. Bits are transmitted one at a time in ]. By contrast, multiple bits are transmitted simultaneously in a ]. A ] 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 ], a ] operates on binary strings as though they are vectors of bits, rather than interpreting them as ]s.

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


=== Storage === === Storage ===
⚫ In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's ], 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 ] or ]. The first electrical devices for discrete logic (such as ] and ] control ], ], and Konrad Zuse's computer) represented bits as the states of ]s which could be either "open" or "closed". When relays were replaced by ]s, starting in the 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a ], charges stored on the inside surface of a ], or opaque spots printed on ] by ] techniques.


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>
⚫ In the 1950s and 1960s, these methods were largely supplanted by ] devices such as ], ]s, ], and ], where a bit was represented by the polarity of ] of a certain area of a ] film, or by a change in polarity from one direction to the other. The same principle was later used in the ] developed in the 1980s, and is still found in various ] items such as ] tickets and some ]s.

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 ] 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>
⚫ In modern ], such as ], the two values of a bit may be represented by two levels of ] stored in a ]. In certain types of ]s and ], a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In ]s, a bit is encoded as the presence or absence of a ] pit on a reflective surface. In one-dimensional ]s, bits are encoded as the thickness of alternating black and white lines.


== Unit and symbol == == Unit and symbol ==
Line 43: Line 54:


=== Multiple bits === === Multiple bits ===
{{redirect|MBit|the technical high school|MBIT}}
{{Quantities of bits}} {{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 ] have traditionally been used. The most common is the unit ], coined by ] in June 1956, which historically was used to represent the group of bits used to encode a single ] of text (until ] 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 ] element in many ]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.{{As of?|date=September 2023}} However, because of the ambiguity of relying on the underlying hardware design, the unit ] was defined to explicitly denote a sequence of eight&nbsp;bits. Multiple bits may be expressed and represented in several ways. For convenience of representing commonly reoccurring groups of bits in information technology, several ] have traditionally been used. The most common is the unit ], coined by ] in June 1956, which historically was used to represent the group of bits used to encode a single ] of text (until ] 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 ] element in many ]s. By 1993, the trend in hardware design had converged on the 8-bit ].<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 ] was defined to explicitly denote a sequence of eight&nbsp;bits.


Computers usually manipulate bits in groups of a fixed size, conventionally named "]". 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. Computers usually manipulate bits in groups of a fixed size, conventionally named "]". 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 ] defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes ] (10<sup>3</sup>) through ] (10<sup>24</sup>) increment by multiples of one thousand, and the corresponding units are the ] (kbit) through the ] (Ybit). The ] defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes ] (10<sup>3</sup>) through ] (10<sup>24</sup>) increment by multiples of one thousand, and the corresponding units are the ] (kbit) through the ] (Ybit).

== Information capacity and information compression ==
{{Update|type=section|date=October 2018|reason=it cites a fact about global information content in computers from 2007}}
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 ] capacity to store binary data ({{mono|0}} or {{mono|1}}, up or down, current or not, etc.).<ref name="Information in small bits"/> Information capacity of a storage system is only an upper bound to the quantity of information stored therein. If the two possible values of one&nbsp;bit of storage are not equally likely, that bit of storage contains less than one&nbsp;bit of information. If the value is completely predictable, then the reading of that value provides no information at all (zero entropic bits, because no resolution of uncertainty occurs and therefore no information is available). If a computer file that uses ''n''&nbsp;bits of storage contains only ''m''&nbsp;<&nbsp;''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 ] 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 ]s of hardware digits. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information.<ref name="Hilbert-Lopez_2011"/> When optimally compressed, the resulting carrying capacity approaches ] or ].<ref name="Information in small bits"/>

== Bit-based computing ==
Certain ] computer ] 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 ]ped computer displays became popular, some computers provided specialized ] 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 ] or ], 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 ] or ] depending on the context.

== Other information units ==
{{Main|Units of information}}
Similar to ] and ] in physics; ] and data storage size have the same ] of ], but there is in general no meaning to adding, subtracting or otherwise combining the units mathematically, although one may act as a bound on the other.

Units of information used in information theory include the '']'' (Sh), the '']'' (nat) and the '']'' (Hart). One shannon is the maximum amount of information needed to specify the state of one bit of storage. These are related by 1&nbsp;Sh ≈ 0.693&nbsp;nat ≈ 0.301&nbsp;Hart.

Some authors also define a '''binit''' as an arbitrary information unit equivalent to some fixed but unspecified number of bits.<ref name="Bhattacharya_2005"/>


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


== References == == References ==
Line 95: Line 87:
<ref name="Abramson_1963">{{cite book |author-first=Norman |author-last=Abramson |date=1963 |title=Information theory and coding |publisher=]}}</ref> <ref name="Abramson_1963">{{cite book |author-first=Norman |author-last=Abramson |date=1963 |title=Information theory and coding |publisher=]}}</ref>
<ref name="NIST_2008">National Institute of Standards and Technology (2008), ''Guide for the Use of the International System of Units''. {{webarchive|url=https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf |date=3 June 2016}}</ref> <ref name="NIST_2008">National Institute of Standards and Technology (2008), ''Guide for the Use of the International System of Units''. {{webarchive|url=https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf |date=3 June 2016}}</ref>
<ref name="Hilbert-Lopez_2011"> {{webarchive|url=https://web.archive.org/web/20130727161911/http://www.sciencemag.org/content/332/6025/60 |date=2013-07-27}}, especially {{webarchive|url=https://web.archive.org/web/20110531133712/http://www.sciencemag.org/content/suppl/2011/02/08/science.1200970.DC1/Hilbert-SOM.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.sciencemag.org/content/suppl/2011/02/08/science.1200970.DC1/Hilbert-SOM.pdf |archive-date=2022-10-09 |url-status=live |date=2011-05-31}}, Martin Hilbert and Priscila López (2011), ], 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html</ref>
<!-- UNUSED REF <ref name="Bush_1936">{{cite journal |author-last=Bush |author-first=Vannevar |author-link=Vannevar Bush |title=Instrumental analysis |journal=] |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> --> <!-- UNUSED REF <ref name="Bush_1936">{{cite journal |author-last=Bush |author-first=Vannevar |author-link=Vannevar Bush |title=Instrumental analysis |journal=] |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=] |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 |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 ].|hdl-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=] |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 ].|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=] |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_1948_2">{{cite journal |author-last=Shannon |author-first=Claude Elwood |author-link=Claude Elwood Shannon |title=A Mathematical Theory of Communication |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=] |date=1949 |isbn=0-252-72548-4 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |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="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=] |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="Information in small bits"> Information in Small Bits is a book produced as part of a non-profit outreach project of the IEEE Information Theory Society.
The book introduces Claude Shannon and basic concepts of Information Theory to children 8 and older using relatable cartoon stories and problem-solving activities.</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 ]'s ] computer as background, handling 64-character words divisible into groups of 8 (I designed the character set for it, under the guidance of Dr. ], the man who DID coin the term "]" for an 8-bit grouping). The ] 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="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 ]'s ] computer as background, handling 64-character words divisible into groups of 8 (I designed the character set for it, under the guidance of Dr. ], the man who DID coin the term "]" for an 8-bit grouping). The ] 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=] Memo No. 39G |publisher=] |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 ], coming from Memory in parallel, into ], or "]s" as we have called them, to be sent to the ] serially. The 60 bits are dumped into ]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 ]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 ] 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_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=] Memo No. 39G |publisher=] |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 ], coming from Memory in parallel, into ], or "]s" as we have called them, to be sent to the ] serially. The 60 bits are dumped into ]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 ]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 ] work, or to handle bytes of only one bit for logical analysis, or to offset the bytes by any number of bits. }}</ref>
Line 107: Line 96:
<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=] / 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="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=] / 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=] |volume=2 |number=9 |pages=19–23 |date=1959 |doi=10.1145/368424.368435|s2cid=36115735 |doi-access=free }}</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=] |volume=2 |number=9 |pages=19–23 |date=1959 |doi=10.1145/368424.368435|s2cid=36115735 |doi-access=free }}</ref>
<ref name="Bhattacharya_2005">{{cite book |author-first=Amitabha |author-last=Bhattacharya |title=Digital Communication |publisher=] |date=2005 |isbn=978-0-07059117-2 |url=https://books.google.com/books?id=0CI8bd0upS4C&pg=PR20 |url-status=live |archive-url=https://web.archive.org/web/20170327011019/https://books.google.com/books?id=0CI8bd0upS4C&pg=PR20&lpg=PR20 |archive-date=2017-03-27}}</ref>
}} }}


Latest revision as of 05:46, 8 January 2025

Unit of information This article is about the unit of information. For other uses, see Bit (disambiguation).

Units of
information
Information-theoretic
Data storage
Quantum information

The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either "1" or "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 storage or device is a matter of convention, and different assignments may be used even within the same device or 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 byte, but historically the size of the byte is not strictly defined. 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 variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known. As a unit of information or negentropy, the bit is also known as a shannon, 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, but this usage is now rare.

In data compression, the goal is to find a shorter representation for a string, so that it requires fewer bits of storage -- but it must be "compressed" before storage and then (generally) "decompressed" before it is used in a computation. 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.

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. Claude E. Shannon first used the word "bit" in his seminal 1948 paper "A Mathematical Theory of Communication". 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".

Physical representation

A bit can be stored by a digital device or other physical system that exists in either of two possible distinct states. These may be the two stable states of a flip-flop, two positions of an electrical switch, two distinct voltage or current levels allowed by a circuit, two distinct levels of light intensity, two directions of magnetization or 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 bit of information. The encoding of text by bits was also used in Morse code (1844) and early digital communications machines such as teletypes and stock ticker machines (1870).

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 relays which could be either "open" or "closed". When relays were replaced by vacuum tubes, 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 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 tapes, drums, and disks, where a bit was represented by the polarity of 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 metro tickets and some credit cards.

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 arrays 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 discs, a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. In one-dimensional bar codes 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 gates.

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, a bitwise operation operates on binary strings as though they are vectors of bits, rather than interpreting them as binary numbers.

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.

Mass storage devices are usually measured in decimal SI multiples, for example 1 TB = 10 12 {\displaystyle 10^{12}} bytes.

Confusingly, the storage capacity of a directly-addressable memory device, such as a 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 2 30 {\displaystyle 2^{30}} 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.

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. However, the lower-case letter 'b' is widely used as well and was recommended by the IEEE 1541 Standard (2002). In contrast, the upper case letter 'B' is the standard and customary symbol for byte.

Multiple bits

"MBit" redirects here. For the technical high school, see MBIT.
Multiple-bit units
Decimal
Value Metric
1000 kbit kilobit
1000 Mbit megabit
1000 Gbit gigabit
1000 Tbit terabit
1000 Pbit petabit
1000 Ebit exabit
1000 Zbit zettabit
1000 Ybit yottabit
1000 Rbit ronnabit
1000 Qbit quettabit
Binary
Value IEC Memory
1024 Kibit kibibit Kbit Kb kilobit
1024 Mibit mebibit Mbit Mb megabit
1024 Gibit gibibit Gbit Gb gigabit
1024 Tibit tebibit —
1024 Pibit pebibit —
1024 Eibit exbibit —
1024 Zibit zebibit —
1024 Yibit yobibit —
—
—
Orders of magnitude of data

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 of text (until UTF-8 multibyte encoding took over) in a computer and for this reason it was used as the basic addressable element in many computer architectures. By 1993, the trend in hardware design had converged on the 8-bit byte. However, because of the ambiguity of relying on the underlying hardware design, the unit octet was defined to explicitly denote a sequence of eight bits.

Computers usually manipulate bits in groups of a fixed size, conventionally named "words". Like the byte, the number of bits in a word also varies with the hardware design, and is typically between 8 and 80 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 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 (10) through yotta (10) increment by multiples of one thousand, and the corresponding units are the kilobit (kbit) through the yottabit (Ybit).

See also

References

  1. Mackenzie, Charles E. (1980). Coded Character Sets, History and Development (PDF). The Systems Programming Series (1 ed.). Addison-Wesley Publishing Company, Inc. p. x. ISBN 978-0-201-14460-4. LCCN 77-90165. Archived (PDF) from the original on May 26, 2016. Retrieved August 25, 2019.
  2. ^ Bemer, Robert William (2000-08-08). "Why is a byte 8 bits? Or is it?". Computer History Vignettes. Archived from the original on 2017-04-03. Retrieved 2017-04-03. With IBM's 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 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.
  3. Anderson, John B.; Johnnesson, Rolf (2006), Understanding Information Transmission
  4. Haykin, Simon (2006), Digital Communications
  5. IEEE Std 260.1-2004
  6. "Units: B". Archived from the original on 2016-05-04.
  7. Breipohl, Arthur M. (1963-08-18). Adaptive Communication Systems. University of New Mexico. p. 7. Retrieved 2025-01-07.
  8. "binit". The Free Dictionary. Retrieved 2025-01-07.
  9. Abramson, Norman (1963). Information theory and coding. McGraw-Hill.
  10. ^ Shannon, Claude Elwood (July 1948). "A Mathematical Theory of Communication" (PDF). Bell System Technical Journal. 27 (3): 379–423. doi:10.1002/j.1538-7305.1948.tb01338.x. hdl:11858/00-001M-0000-002C-4314-2. Archived from the original (PDF) on 1998-07-15 – via Bell Labs Computing and Mathematical Sciences Research. 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 J. W. Tukey.
  11. Shannon, Claude Elwood (October 1948). "A Mathematical Theory of Communication". Bell System Technical Journal. 27 (4): 623–666. doi:10.1002/j.1538-7305.1948.tb00917.x. hdl:11858/00-001M-0000-002C-4314-2.
  12. Shannon, Claude Elwood; Weaver, Warren (1949). A Mathematical Theory of Communication (PDF). University of Illinois Press. ISBN 0-252-72548-4. Archived from the original (PDF) on 1998-07-15 – via Bell Labs Computing and Mathematical Sciences Research.
  13. "UnitsPolicy - Ubuntu Wiki". Retrieved 2025-01-07.
  14. "Use MB/GB/TB suffix for VM memory input". Github Netbox Community. 2022. Retrieved 2025-01-08.
  15. National Institute of Standards and Technology (2008), Guide for the Use of the International System of Units. Online version. Archived 3 June 2016 at the Wayback Machine
  16. Buchholz, Werner (1956-06-11). "7. The Shift Matrix" (PDF). The Link System. IBM. pp. 5–6. Stretch Memo No. 39G. Archived (PDF) from the original on 2017-04-04. Retrieved 2016-04-04. 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, coming from Memory in parallel, into characters, or "bytes" as we have called them, to be sent to the Adder serially. The 60 bits are dumped into magnetic cores 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 digits, 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.
  17. Buchholz, Werner (February 1977). "The Word "Byte" Comes of Age..." Byte Magazine. 2 (2): 144. The first reference found in the files was contained in an internal memo written in June 1956 during the early days of developing 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 G A Blaauw, F P Brooks Jr and W Buchholz in the IRE Transactions on Electronic Computers, June 1959, page 121. The notions of that paper were elaborated in Chapter 4 of Planning a Computer System (Project Stretch), edited by W Buchholz, McGraw-Hill Book Company (1962). The rationale for coining the term was explained there on page 40 as follows:
    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.)
    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.
  18. Blaauw, Gerrit Anne; Brooks, Jr., Frederick Phillips; Buchholz, Werner (1962), "Chapter 4: Natural Data Units" (PDF), in Buchholz, Werner (ed.), Planning a Computer System – Project Stretch, McGraw-Hill Book Company, Inc. / The Maple Press Company, York, PA., pp. 39–40, LCCN 61-10466, archived from the original (PDF) on 2017-04-03, retrieved 2017-04-03
  19. Bemer, Robert William (1959). "A proposal for a generalized card code of 256 characters". Communications of the ACM. 2 (9): 19–23. doi:10.1145/368424.368435. S2CID 36115735.
  20. "ISO/IEC 2382-1:1993(en) Information technology — Vocabulary — Part 1: Fundamental terms". p. 01.02.09. Retrieved 2025-01-08.

External links

  • Bit Calculator – a tool providing conversions between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte
  • BitXByteConverter Archived 2016-04-06 at the Wayback Machine – a tool for computing file sizes, storage capacity, and digital information in various units
Units of information
Platform-independent units
Platform-dependent units
Metric bit units
Metric byte units
Data types
Uninterpreted
Numeric
Pointer
Text
Composite
Other
Related
topics
Categories: