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{{short description|Unit of information}} |
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{{About|the unit of information}} |
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{{Refimprove|date=January 2008}} |
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{{Use dmy dates|date=December 2020|cs1-dates=y}} |
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{{Fundamental info units}} |
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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. |
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A '''bit''' is a [[binary numeral system|'''b'''inary]] [[numerical digit|dig'''it''']], taking a logical value of either "1" or "0" (also referred to as "true" or "false" respectively). Binary digits are a basic unit of [[information]] [[Computer data storage|storage]] and [[transmission (telecommunications)|communication]] in digital [[computing]] and digital [[information theory]]. Information theory also often uses the natural digit, called either a ''[[Nat (information)|nit]]'' or a ''[[Nat (information)|nat]]''. [[Quantum computing]] uses [[qubit]]s; single piece of quantum information encoded on a two level quantum system and hence having the potential to exist in [[quantum superposition|superposition]] of "true" and "false". |
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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. |
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The bit is also a unit of measurement, the information capacity of one binary digit. It has the symbol '''bit''' or '''b''', the latter recommended by [[IEEE 1541-2002]]. |
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A contiguous group of binary digits is commonly called a ''[[bit string]]'', a bit vector, or a single-dimensional (or multi-dimensional) ''[[bit array]]''. |
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==Binary digit== |
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A group of eight bits is called one ''[[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]]''. |
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[[Claude E. Shannon]] first used the word '''''bit''''' in his 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 digit" to simply "bit". Interestingly, [[Vannevar Bush]] had written in 1936 of "bits of information" that could be stored on the [[punch card]]s used in the mechanical computers of that time. <ref>''Darwin among the machines: the evolution of global intelligence'', [[George Dyson (science historian)|George Dyson]], 1997. ISBN 0-201-40649-7</ref> |
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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]], the bit is also known as a ''[[shannon (unit)|shannon]]'',<ref name="Rowlett"/> named after [[Claude E. Shannon]]. |
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A bit of storage can be either on (1) or off (0). A single bit is a one or a zero, a true or a false, a "flag" which is "on" or "off", or in general, the quantity of information required to distinguish two mutually exclusive equally probable ''[[State (computer science)|state]]s'' from each other. [[Gregory Bateson]] defined a bit as "a difference which makes a difference".<ref>[http://plato.acadiau.ca/courses/educ/reid/papers/PME25-WS4/SEM.html Social Systems<!-- Bot generated title -->]</ref> |
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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. |
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==Representation==<!-- Warning: this heading is the target of a link in [[Flip-flop (electronics)]] --> |
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===Transmission=== |
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Bits can be implemented in many forms depending on the requirements in an application context. For example, in [[digital circuit]]ry in most computing devices as well as flash memories, a bit is an [[electric]]al pulse generated by the internal clock in the control unit or data register. For devices using [[positive logic]], a logical 1 (true value or high) is represented by up to 5 [[volt]]s (in the case of TTL circuitry), while a logical 0 (false value or low) is represented by 0 volts. |
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== |
== History == |
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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 [[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 [[Teleprinter|teletypes]] and [[stock ticker machine]]s (1870). |
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Bits are manipulated in the [[volatile memory]] of a computer, and can further be encoded in a persistent manner on a [[magnetic storage]] device such as tape or disc, as well as on [[optical disc]]s or stored in non-volatile [[flash memory]]. |
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[[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"/> |
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==Unit== |
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It is important to differentiate between the use of ''bit'' in referring to physical data storage and its use in referring to a statistical unit of information. The bit, as a storage entity, can store only the values 0 and 1 by design. A statistical bit is the amount of information that, ''on average''{{Fact|date=September 2007}}, can be stored in a discrete bit. It is thus the amount of information carried by a choice between two equally likely outcomes. One bit corresponds to about 0.693 [[nat (information)|nat]]s (ln(2)), or 0.301 [[ban (information)|hartley]]s (log<sub>10</sub>(2)). |
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== Physical representation <span class="anchor" id="Representation"></span> == |
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Consider, for example, a [[computer file]] with one thousand 0s and 1s which can be [[lossless data compression|losslessly compressed]] to a file of five hundred 0s and 1s (on average, over all files of that kind). The original file, although having 1000 bits of storage, has at most 500 bits of [[information entropy]], since information is not destroyed by lossless compression. A file can have no more information theoretical bits than it has storage bits. If these two ideas need to be distinguished, sometimes the name ''bit'' is used when discussing data storage while ''shannon'' is used for the statistical bit.{{Fact|date=May 2009}} However, most of the time, the meaning is clear from the context. |
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<!-- Warning: this heading is the target of a link in [[Flip-flop (electronics)]] --> |
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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. |
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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 circuit. |
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==Abbreviation and symbol== |
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[[IEEE 1541-2002]] specifies "b" to be the unit symbol for bit and "B" to be that for byte. This convention is also widely used in computing. |
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For devices using [[positive logic]], 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 [[transistor–transistor logic]] (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 V and no lower than 2.6 V, respectively; while TTL inputs are specified to recognize 0.8 V or below as {{mono|0}} and 2.2 V or above as {{mono|1}}. |
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The relevant ISO/IEC standard is [[ISO/IEC 80000|IEC 80000-13:2008]] which is not publicly available. ISO says: "This standard cancels and replaces subclauses 3.8 and 3.9 of IEC 60027-2:2005. The only significant change is the addition of explicit definitions for some quantities."<ref>http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31898</ref> |
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=== Transmission and processing === |
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These subclauses were related to information theory and prefixes for binary multiples. |
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Bits are transmitted one at a time in [[serial transmission]], and by a multiple number of bits in [[parallel transmission]]. A [[bitwise operation]] optionally processes 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. |
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=== Storage === |
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The [[International Electrotechnical Commission]]'s [[IEC 60027]], specifies that the bit should have the symbol ''bit'', used in all multiples, such as "kbit" (for kilobit). In the same documents, the symbols "o" and "B" are specified for the [[byte]]. |
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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 [[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. |
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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. |
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[[NIST]] in their "''Guide for the Use of the International System of Units'' Edition 2008" recommends "bit" while referring to obsolete [[ISO 31]] and [[IEC 60027]].<ref>http://physics.nist.gov/cuu/pdf/sp811.pdf</ref> |
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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. |
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== Unit and symbol == |
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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. |
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=== Multiple bits === |
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{{redirect|MBit|the technical high school|MBIT}} |
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{{Quantities of bits}} |
{{Quantities of bits}} |
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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 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 [[Octet (computing)|octet]] was defined to explicitly denote a sequence of eight bits. |
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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 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. |
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==Multiple bits== |
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Several naming conventions exist for collections or groups of bits. The [[byte]], although historically differing in size depending on computer hardware architecture, is today almost always eight bits. However, 8-bit bytes are also known specifically as ''[[octet (computing)|octet]]s''. These can represent 256 (2<sup>8</sup>, 0–255) values. A 4-bit quantity is known as a ''[[nibble]]'', and can represent 16 (2<sup>4</sup>, 0–15) values. |
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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). |
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"[[Word (computing)|Word]]" is a term for a slightly larger group of bits, but it has no standard size. It represents the size of one register in a [[Computer]]-[[CPU]]. In the [[IA-32]] architecture more commonly known as x86-32, 16 bits constitute a ''word'' (with 32 bits being a double-word or [[Word (computer science)#Dword and Qword|dword]]), but other architectures have word sizes of 8, 32, 64, 80 bits or others. |
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== Information capacity and information compression == |
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Terms for large quantities of bits can be formed using the standard range of SI prefixes, e.g., [[kilo]]bit ([[kbit]]), [[mega]]bit ([[Mbit]]) and [[giga]]bit ([[Gbit]]), or using any of the [[binary prefixes]]. Much confusion exists regarding these units and their abbreviations, due to the historical usage of SI-prefixes for binary multiples (1024-radix) and attempts to define a consistent standard. |
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{{Update|type=section|date=October 2018|reason=it cites a fact about global information content in computers from 2007}} |
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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 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 bit of storage are not equally likely, that bit of storage contains less than one 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'' bits of storage contains only ''m'' < ''n'' bits of information, then that information can in principle be encoded in about ''m'' 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. |
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For example, it is estimated that the combined technological capacity of the world to store information provides 1,300 [[exabyte]]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 [[Shannon information]] or [[information entropy]].<ref name="Information in small bits"/> |
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When a bit within a group of bits such as a byte or word is to be referred to, it is usually specified by a number from 0 (not 1) upwards corresponding to its position within the byte or word. However, 0 can refer to either the [[most significant bit]] or to the [[least significant bit]] depending on the context, so the convention of use must be known. |
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== Bit-based computing == |
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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. |
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. |
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In the 1980s, when [[bitmap]]ped computer displays became popular, some computers provided specialized [[bitblt|bit block transfer]] instructions to set or copy the bits that corresponded to a given rectangular area on the screen. |
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[[Telecommunications]] or [[computer network]] transfer rates are usually described in terms of [[bits per second]] (''bit/s''), not to be confused with [[baud]]. |
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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. |
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===Uncommon names for groups of bits=== |
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Similarly to the well-known terms ''byte'' and ''nibble'', other terms of bit groups of varying sizes have been used over time.<ref>[http://dictionary.reference.com/browse/nybble nybble] reference.com sourced from Jargon File 4.2.0, accessed 2007-08-12</ref> All of these are [[jargon]], are obsolete, or are not very common. |
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== Other information units == |
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*1 bit: sniff |
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{{Main|Units of information}} |
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*2 bits: lick, crumb, quad, quarter, tayste, tydbit |
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Similar to [[torque]] and [[energy]] in physics; [[Information#Information theory|information-theoretic information]] and data storage size have the same [[Dimensional analysis|dimensionality]] of [[Unit of measurement|units of measurement]], 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. |
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*4 bits: [[nibble]], nybble |
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*5 bits: nickel, nyckle |
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*10 bits: [[deckle]], dyme bag |
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*16 bits: plate, playte, [[Chomp (disambiguation)|chomp]], chawmp (on a 32-bit machine) |
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*18 bits: chomp, chawmp (on a 36-bit machine) |
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*32 bits: dinner, dynner, gawble (on a 32-bit machine) |
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*48 bits: [[gobble]], gawble (under circumstances that remain obscure) |
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Units of information used in information theory include the ''[[shannon (unit)|shannon]]'' (Sh), the ''[[nat (unit)|natural unit of information]]'' (nat) and the ''[[hartley (unit)|hartley]]'' (Hart). One shannon is the maximum amount of information needed to specify the state of one bit of storage. These are related by 1 Sh ≈ 0.693 nat ≈ 0.301 Hart. |
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==See also== |
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*[[Units of information]] |
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*[[Byte]] |
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*[[Integral data type]] |
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*[[Primitive type]] |
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*[[Bitstream]] |
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*[[Information entropy]] |
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*[[Binary arithmetic]] |
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*[[Ternary numeral system]] |
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Some authors also define a '''binit''' as an arbitrary information unit equivalent to some fixed but unspecified number of bits.<ref name="Bhattacharya_2005"/> |
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==References== |
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{{reflist}} |
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== |
== See also == |
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* {{Annotated link|Baud}} |
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* [http://www.bit-calculator.com Bit Calculator - Convert between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte] |
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* {{Annotated link|Binary numeral system}} |
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* {{Annotated link|Bit rate}} |
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* {{Annotated link|Bitstream}} |
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* {{Annotated link|Byte}} |
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* {{Annotated link|Entropy (information theory)}} |
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* {{Annotated link|Fuzzy bit}} |
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* {{Annotated link|Integer (computer science)}} |
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* {{Annotated link|Nibble}} |
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* {{Annotated link|Primitive data type}} |
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* {{Annotated link|Qubit}} (quantum bit) |
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* {{Annotated link|Shannon (unit)}} |
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* {{Annotated link|Ternary numeral system}} |
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* {{Annotated link|Trit (computing)}} (Trinary digit) |
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== References == |
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{{Computer Storage Volumes}} |
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{{reflist|refs= |
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<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> |
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<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> |
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<ref name="Haykin_2006">{{citation |author-first=Simon |author-last=Haykin |date=2006 |title=Digital Communications}}</ref> |
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<ref name="IEEE_260">[[IEEE Std 260.1-2004]]</ref> |
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<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> |
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<ref name="Abramson_1963">{{cite book |author-first=Norman |author-last=Abramson |date=1963 |title=Information theory and coding |publisher=[[McGraw-Hill]]}}</ref> |
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<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> |
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<ref name="Hilbert-Lopez_2011">[https://www.science.org/doi/10.1126/science.1200970 "The World's Technological Capacity to Store, Communicate, and Compute Information"] {{webarchive|url=https://web.archive.org/web/20130727161911/http://www.sciencemag.org/content/332/6025/60 |date=2013-07-27}}, especially [https://www.science.org/doi/10.1126/science.1200970 Supporting online material] {{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), [[Science (journal)|Science]], 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html</ref> |
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<!-- 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> --> |
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<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 |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> |
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<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> |
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<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 |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> |
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<ref name="Information in small bits">{{usurped|1=[https://web.archive.org/web/20180731213543/https://informationinsmallbits.com/ 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. |
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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> |
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<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> |
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<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> |
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<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 A Blaauw]], [[Frederick Phillips Brooks, Jr.|F P Brooks Jr]] and [[Werner Buchholz|W 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 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> |
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<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> |
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<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> |
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<ref name="Bhattacharya_2005">{{cite book |author-first=Amitabha |author-last=Bhattacharya |title=Digital Communication |publisher=[[Tata McGraw-Hill Education]] |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> |
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}} |
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== External links == |
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{{wiktionary}} |
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* [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 |
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* [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 |
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{{Information units}} |
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{{Data types}} |
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{{Authority control}} |
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Latest revision as of 09:03, 23 December 2024
Units of information |
Information-theoretic |
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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.[1] 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.[2] 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,[3] or the information that is gained when the value of such a variable becomes known.[4][5] As a unit of information, the bit is also known as a shannon,[6] named after Claude E. Shannon.
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
[edit]The encoding of data by discrete bits was used in the punched cards 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).
Ralph Hartley suggested the use of a logarithmic measure of information in 1928.[7] Claude E. Shannon first used the word "bit" in his seminal 1948 paper "A Mathematical Theory of Communication".[8][9][10] 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".[8]
Physical representation
[edit]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.
Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an electrical voltage or current pulse, or by the electrical state of a 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. Different logic families require different voltages, and variations are allowed to account 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 V and no lower than 2.6 V, respectively; while TTL inputs are specified to recognize 0.8 V or below as 0 and 2.2 V or above as 1.
Transmission and processing
[edit]Bits are transmitted one at a time in serial transmission, and by a multiple number of bits in parallel transmission. A bitwise operation optionally processes 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
[edit]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 paper card or 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 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, 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 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, bits are encoded as the thickness of alternating black and white lines.
Unit and symbol
[edit]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.[11] 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
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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[2][12][13][14][15] and for this reason it was used as the basic addressable element in many computer architectures. The trend in hardware design converged on the most common implementation of using eight bits per byte, as it is widely used today.[as of?] 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 (103) through yotta (1024) increment by multiples of one thousand, and the corresponding units are the kilobit (kbit) through the yottabit (Ybit).
Information capacity and information compression
[edit]This article needs to be updated. The reason given is: it cites a fact about global information content in computers from 2007.(October 2018) |
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 data (0 or 1, up or down, current or not, etc.).[16] 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 bit of storage are not equally likely, that bit of storage contains less than one 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 bits of storage contains only m < n bits of information, then that information can in principle be encoded in about m bits, at least on the average. This principle is the basis of 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. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information.[17] When optimally compressed, the resulting carrying capacity approaches Shannon information or information entropy.[16]
Bit-based computing
[edit]Certain bitwise computer 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 bitmapped computer displays became popular, some computers provided specialized bit block transfer 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 or least significant bit depending on the context.
Other information units
[edit]Similar to torque and energy in physics; information-theoretic information and data storage size have the same dimensionality of units of measurement, 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 shannon (Sh), the natural unit of information (nat) and the hartley (Hart). One shannon is the maximum amount of information needed to specify the state of one bit of storage. These are related by 1 Sh ≈ 0.693 nat ≈ 0.301 Hart.
Some authors also define a binit as an arbitrary information unit equivalent to some fixed but unspecified number of bits.[18]
See also
[edit]- Baud – Symbol rate measurement in telecommunications
- Binary numeral system – Number expressed in the base-2 numeral system
- Bit rate – Information transmission rate expressed in bits per second
- Bitstream – Sequence of binary digits
- Byte – Unit of digital information, usually 8 bits
- Entropy (information theory) – Expected amount of information needed to specify the output of a stochastic data source
- Fuzzy bit
- Integer (computer science) – Datum of integral data type
- Nibble – Four-bit unit of binary data
- Primitive data type – An extremely basic/core data type provided by a programming language
- Qubit – Basic unit of quantum information (quantum bit)
- Shannon (unit) – Unit of information
- Ternary numeral system – Base-3 numeral system
- Trit (computing) – Base-3 numeral system (Trinary digit)
References
[edit]- ^ 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.
- ^ a b 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. […]
- ^ Anderson, John B.; Johnnesson, Rolf (2006), Understanding Information Transmission
- ^ Haykin, Simon (2006), Digital Communications
- ^ IEEE Std 260.1-2004
- ^ "Units: B". Archived from the original on 2016-05-04.
- ^ Abramson, Norman (1963). Information theory and coding. McGraw-Hill.
- ^ a b 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.
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.
- ^ 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.
- ^ 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.
- ^ 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
- ^ 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. […]
- ^ 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. […] - ^ 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
- ^ 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.
- ^ a b Information in small bits[usurped] 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.
- ^ "The World's Technological Capacity to Store, Communicate, and Compute Information" Archived 2013-07-27 at the Wayback Machine, especially Supporting online material Archived 2011-05-31 at the Wayback Machine, Martin Hilbert and Priscila López (2011), Science, 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html
- ^ Bhattacharya, Amitabha (2005). Digital Communication. Tata McGraw-Hill Education. ISBN 978-0-07059117-2. Archived from the original on 2017-03-27.
External links
[edit]- 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