Bit: Difference between revisions
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{{otheruses1|the unit of information}} |
{{otheruses1|the unit of information}} |
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In [[computing]] and [[telecommunication]]s a '''bit''' is a basic unit of [[information]] [[computer data storage|storage]] and [[transmission (telecommunications)|communication]]; it is the maximum amount of information that can be stored by a device or other physical system that can normally exist in only two distinct [[state (computer science)|states]]. These states are often interpreted (especially in the storage of [[number|numerical data]]) as the [[binary numeral system|'''b'''inary]] [[numerical digit|dig'''it''']]s 0 and 1. They may be interpreted also as [[logical value]]s, either "true" or "false"; or two settings of a [[flag (computing)|flag]] or [[electric switch|switch]], either "on" or "off". |
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{{Refimprove|date=January 2008}} |
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In [[information theory]], "one bit" is typically defined as the uncertainty of a binary random variable that is 0 or 1 with equal probability,<ref>John B. Anderson, Rolf Johnnesson (2006) ''Understanding Information Transmission''.</ref> or the information that is gained when the value of such a variable becomes known.<ref>Simon Haykin (2006), ''Digital Communications''</ref> |
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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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In [[quantum computing]], a '''quantum bit''' or '''[[qubit]]''' is a [[quantum mechanics|quantum system]] that can exist in [[quantum superposition|superposition]] of two bit values, "true" and "false". |
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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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The symbol for bit, as a unit of information, is "bit" or (lowercase) "b"; the latter being recommended by the [[IEEE 1541-2002|IEEE 1541 Standard (2002)]]. |
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==Binary digit== |
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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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==History== |
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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 encoding of data by discrete bits was used in the the [[punched card]]s invented by [[Jacquard]] and adopted by [[Charles Babbage]] and [[Hermann Hollerith]]. In all those systems, each card conceptually carried an array of hole positions; each position could be either punched through or not, thus carrying one bit of information. |
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| ⚫ | [[E . V. Hartley]] suggested the use of a logarithmic measure of information in 1928.<ref name="abramson">Norman Abramson (1963), ''Information theory and coding''. McGraw-Hill.</ref> [[Claude E. Shannon]] first used the word '''''bit''''' in his seminal 1948 paper ''[[A Mathematical Theory of Communication]]''. 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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==Representation==<!-- Warning: this heading is the target of a link in [[Flip-flop (electronics)]] --> |
==Representation==<!-- Warning: this heading is the target of a link in [[Flip-flop (electronics)]] --> |
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===Transmission=== |
===Transmission and processing=== |
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Bits can be implemented in many forms |
Bits can be implemented in many forms. In most modern computing devices, a bit is usually represented by an [[electric]]al [[voltage]] or [[current]] pulse, or by the electrical state of a [[flip-flop (electronics)|flip-flop circuit]]. For devices using [[positive logic]], a digit value of 1 (true value or high) is represented by a positive voltage relative to the [[electrical ground]] voltage (up to 5 [[volt]]s in the case of [[transitor-transistor logic|TTL]] designs), while a digit value of 0 (false value or low) is represented by 0 volts. |
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===Storage=== |
===Storage=== |
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In [[semiconductor memory]], such as [[dynamic random-access memory]] or [[flash memory]], the two values of a bit may be represented by two levels of [[electrical charge]] stored in a [[capacitor]]. In [[programmable logic array]]s and certain types of [[read-only memory]], a bit may be respresented by the presence or absence of a conducting path at a certain point of a curcuit. In [[magnetic storage]] devices such as [[magnetic tape]], [[magnetic disc]], or [[magnetic bubble memory]], it may be represented by the polarity of [[magnetism|magnetization]] of a certain area of a [[ferromagnetic]] film. In [[optical disc]]s, a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. |
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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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==Information capacity and information content== |
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==Unit== |
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Information ''capacity'' of a storage system is only an upper bound to the actual ''quantity of information'' stored therein. If the two possible values of one bit of storage are not equally likely, that bit of storage will contain less than one bit of information. Indeed, if the value is completely predictable, then the reading of that value will provide no information at all (zero bits). 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. Sometimes the name ''bit'' is used when discussing data storage while ''shannon'' is used for the statistical bit.{{Fact|date=May 2009}} |
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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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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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==Abbreviation and symbol== |
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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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{{merge-to|units of information}} |
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{{Quantities of bits}} |
{{Quantities of 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. |
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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[[Telecommunications]] or [[computer network]] transfer rates are usually described in terms of [[bits per second]] (''bit/s''), not to be confused with [[baud]]. |
[[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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===Abbreviations and symbols=== |
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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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===Uncommon names for groups of bits=== |
===Uncommon names for groups of bits=== |
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*32 bits: dinner, dynner, gawble (on a 32-bit machine) |
*32 bits: dinner, dynner, gawble (on a 32-bit machine) |
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*48 bits: [[gobble]], gawble (under circumstances that remain obscure) |
*48 bits: [[gobble]], gawble (under circumstances that remain obscure) |
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==Other information units== |
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Other units of information, sometimes used in information theory, include the ''natural digit'' also called a ''[[nat (information)|nat]]'' or ''nit'' and defined as [[logarithm|log]]<sub>2</sub> ''e'' (≈ 1.443) bits, where ''e'' is the [[e (mathematical constant)|base of the natural logarithms]]; and the ''decit'', ''[[ban (information)|ban]]'' or ''Hartley'', defined as log<sub>2</sub>10 (≈ 3.322) bits.<ref name="abramson"/>. Conversely, one bit of information corresponds to about [[natural logarithm|ln]] 2 (≈ 0.693) nats, or log<sub>10</sub> 2 (≈ 0.301) Hartleys. Some authors also define a '''binit''' as an arbitrary information unit equivalent to some fixed but unspecified number of bits.<ref>Amitabha Bhattacharya, ''Digital Communication''</ref>) |
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==See also== |
==See also== |
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Revision as of 08:07, 2 July 2009
In computing and telecommunications a bit is a basic unit of information storage and communication; it is the maximum amount of information that can be stored by a device or other physical system that can normally exist in only two distinct states. These states are often interpreted (especially in the storage of numerical data) as the binary digits 0 and 1. They may be interpreted also as logical values, either "true" or "false"; or two settings of a flag or switch, either "on" or "off".
In information theory, "one bit" is typically defined as the uncertainty of a binary random variable that is 0 or 1 with equal probability,[1] or the information that is gained when the value of such a variable becomes known.[2]
In quantum computing, a quantum bit or qubit is a quantum system that can exist in superposition of two bit values, "true" and "false".
The symbol for bit, as a unit of information, is "bit" or (lowercase) "b"; the latter being recommended by the IEEE 1541 Standard (2002).
History
The encoding of data by discrete bits was used in the the punched cards invented by Jacquard and adopted by Charles Babbage and Hermann Hollerith. In all those systems, each card conceptually carried an array of hole positions; each position could be either punched through or not, thus carrying one bit of information.
E . V. Hartley suggested the use of a logarithmic measure of information in 1928.[3] 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 digit" to simply "bit". Interestingly, Vannevar Bush had written in 1936 of "bits of information" that could be stored on the punch cards used in the mechanical computers of that time. [4]
Representation
Transmission and processing
Bits can be implemented in many 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 (true value or high) is represented by a positive voltage relative to the electrical ground voltage (up to 5 volts in the case of TTL designs), while a digit value of 0 (false value or low) is represented by 0 volts.
Storage
In semiconductor memory, such as dynamic random-access memory or flash memory, the two values of a bit may be represented by two levels of electrical charge stored in a capacitor. In programmable logic arrays and certain types of read-only memory, a bit may be respresented by the presence or absence of a conducting path at a certain point of a curcuit. In magnetic storage devices such as magnetic tape, magnetic disc, or magnetic bubble memory, it may be represented by the polarity of magnetization of a certain area of a ferromagnetic film. In optical discs, a bit is encoded as the presence or absence of a microscopic pit on a reflective surface.
Information capacity and information content
Information capacity of a storage system is only an upper bound to the actual quantity of information stored therein. If the two possible values of one bit of storage are not equally likely, that bit of storage will contain less than one bit of information. Indeed, if the value is completely predictable, then the reading of that value will provide no information at all (zero bits). 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. Sometimes the name bit is used when discussing data storage while shannon is used for the statistical bit.[citation needed]
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 octets. These can represent 256 (28, 0–255) values. A 4-bit quantity is known as a nibble, and can represent 16 (24, 0–15) values.
"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 dword), but other architectures have word sizes of 8, 32, 64, 80 bits or others.
Terms for large quantities of bits can be formed using the standard range of SI prefixes, e.g., kilobit (kbit), megabit (Mbit) and gigabit (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.
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.
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.
Telecommunications or computer network transfer rates are usually described in terms of bits per second (bit/s), not to be confused with baud.
Abbreviations and symbols
IEEE 1541-2002 specifies "B" to be that for byte. This convention is also widely used in computing.
The relevant ISO/IEC standard is 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."[5]
These subclauses were related to information theory and prefixes for binary multiples.
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.
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.[6]
Uncommon names for groups of bits
Similarly to the well-known terms byte and nibble, other terms of bit groups of varying sizes have been used over time.[7] All of these are jargon, are obsolete, or are not very common.
- 1 bit: sniff
- 2 bits: lick, crumb, quad, quarter, tayste, tydbit
- 4 bits: nibble, nybble
- 5 bits: nickel, nyckle
- 10 bits: deckle, dyme bag
- 16 bits: plate, playte, chomp, chawmp (on a 32-bit machine)
- 18 bits: chomp, chawmp (on a 36-bit machine)
- 32 bits: dinner, dynner, gawble (on a 32-bit machine)
- 48 bits: gobble, gawble (under circumstances that remain obscure)
Other information units
Other units of information, sometimes used in information theory, include the natural digit also called a nat or nit and defined as log2 e (≈ 1.443) bits, where e is the base of the natural logarithms; and the decit, ban or Hartley, defined as log210 (≈ 3.322) bits.[3]. Conversely, one bit of information corresponds to about ln 2 (≈ 0.693) nats, or log10 2 (≈ 0.301) Hartleys. Some authors also define a binit as an arbitrary information unit equivalent to some fixed but unspecified number of bits.[8])
See also
- Units of information
- Byte
- Integral data type
- Primitive type
- Bitstream
- Information entropy
- Binary arithmetic
- Ternary numeral system
References
- ^ John B. Anderson, Rolf Johnnesson (2006) Understanding Information Transmission.
- ^ Simon Haykin (2006), Digital Communications
- ^ a b Norman Abramson (1963), Information theory and coding. McGraw-Hill.
- ^ Darwin among the machines: the evolution of global intelligence, George Dyson, 1997. ISBN 0-201-40649-7
- ^ http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31898
- ^ http://physics.nist.gov/cuu/pdf/sp811.pdf
- ^ nybble reference.com sourced from Jargon File 4.2.0, accessed 2007-08-12
- ^ Amitabha Bhattacharya, Digital Communication