Bit

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

"Qbit (quettabit)" redirects here. For quantum bits, seeQubit.

Thebitis the most basicunit of informationincomputingand digitalcommunication.The name is aportmanteauofbinary digit.The bit represents alogical statewith one of two possiblevalues.These values are most commonly represented as either"1"or"0",but other representations such astrue/false,yes/no,on/off,or+/−are also widely used.

The relation between these values and the physical states of the underlyingstorageordeviceis a matter of convention, and different assignments may be used even within the same device orprogram.It may be physically implemented with a two-state device.

A contiguous group of binary digits is commonly called abit string,a bit vector, or a single-dimensional (or multi-dimensional)bit array. A group of eight bits is called onebyte,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 anibble.

Ininformation theory,one bit is theinformation entropyof a randombinaryvariable that is 0 or 1 with equal probability,or the information that is gained when the value of such a variable becomes known.As aunit of information,the bit is also known as ashannon,named afterClaude E. Shannon.

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

History

The encoding of data by discrete bits was used in thepunched cardsinvented byBasile Bouchonand Jean-Baptiste Falcon (1732), developed byJoseph Marie Jacquard(1804), and later adopted bySemyon Korsakov,Charles Babbage,Herman Hollerith,and early computer manufacturers likeIBM.A variant of that idea was the perforatedpaper 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 inMorse code(1844) and early digital communications machines such asteletypesandstock ticker machines(1870).

Ralph Hartleysuggested the use of a logarithmic measure of information in 1928.Claude E. Shannonfirst used the word "bit" in his seminal 1948 paper "A Mathematical Theory of Communication".He attributed its origin toJohn 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 distinctstates.These may be the two stable states of aflip-flop,two positions of anelectrical switch,two distinctvoltageorcurrentlevels allowed by acircuit,two distinct levels oflight intensity,two directions ofmagnetizationorpolarization,the orientation of reversible double strandedDNA,etc.

Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by anelectricalvoltageorcurrentpulse, or by the electrical state of a flip-flop circuit.

For devices usingpositive logic,a digit value of1(or a logical value of true) is represented by a more positive voltage relative to the representation of0.Different logic families require different voltages, and variations are allowed to account for component aging and noise immunity. For example, intransistor–transistor logic(TTL) and compatible circuits, digit values0and1at 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 as0and 2.2 V or above as1.

Transmission and processing

Bits are transmitted one at a time inserial transmission,and by a multiple number of bits inparallel transmission.Abitwise operationoptionally processes bits one at a time. Data transfer rates are usually measured in decimal SI multiples of the unitbit per second(bit/s), such as kbit/s.

Storage

In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage'sAnalytical 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 apaper cardortape.The first electrical devices for discrete logic (such aselevatorandtraffic lightcontrolcircuits,telephone switches,and Konrad Zuse's computer) represented bits as the states ofelectrical relayswhich could be either "open" or "closed". When relays were replaced byvacuum tubes,starting in the 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down amercury delay line,charges stored on the inside surface of acathode-ray tube,or opaque spots printed onglass discsbyphotolithographictechniques.

In the 1950s and 1960s, these methods were largely supplanted bymagnetic storagedevices such asmagnetic-core memory,magnetic tapes,drums,anddisks,where a bit was represented by the polarity ofmagnetizationof a certain area of aferromagneticfilm, or by a change in polarity from one direction to the other. The same principle was later used in themagnetic bubble memorydeveloped in the 1980s, and is still found in variousmagnetic stripitems such asmetrotickets and somecredit cards.

In modernsemiconductor memory,such asdynamic random-access memory,the two values of a bit may be represented by two levels ofelectric chargestored in acapacitor.In certain types ofprogrammable logic arraysandread-only memory,a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. Inoptical discs,a bit is encoded as the presence or absence of amicroscopicpit on a reflective surface. In one-dimensionalbar codes,bits are encoded as the thickness of alternating black and white lines.

Unit and symbol

The bit is not defined in theInternational System of Units(SI). However, theInternational Electrotechnical Commissionissued standardIEC 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 theIEEE 1541 Standard (2002).In contrast, the upper case letter 'B' is the standard and customary symbol for byte.

Multiple bits

Multiple-bit units
Decimal Value Metric 1000 kbit kilobit 10002 Mbit megabit 10003 Gbit gigabit 10004 Tbit terabit 10005 Pbit petabit 10006 Ebit exabit 10007 Zbit zettabit 10008 Ybit yottabit 10009 Rbit ronnabit 100010 Qbit quettabit	Binary Value IEC Memory 1024 Kibit kibibit Kbit Kb kilobit 10242 Mibit mebibit Mbit Mb megabit 10243 Gibit gibibit Gbit Gb gigabit 10244 Tibit tebibit — 10245 Pibit pebibit — 10246 Eibit exbibit — 10247 Zibit zebibit — 10248 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, severalunits of informationhave traditionally been used. The most common is the unitbyte,coined byWerner Buchholzin June 1956, which historically was used to represent the group of bits used to encode a singlecharacterof text (untilUTF-8multibyte encoding took over) in a computerand for this reason it was used as the basicaddressableelement in manycomputer architectures.The trend in hardware design converged on the most common implementation of using eight bits per byte, as it is widely used today.However, because of the ambiguity of relying on the underlying hardware design, the unitoctetwas 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.

TheInternational System of Unitsdefines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixeskilo(10³) throughyotta(10²⁴) increment by multiples of one thousand, and the corresponding units are thekilobit(kbit) through theyottabit(Ybit).

Information capacity and information compression

When the information capacity of a storage system or a communication channel is presented inbitsorbits per second,this often refers to binary digits, which is acomputer hardwarecapacity to store binary data (0or1,up or down, current or not, etc.).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 usesnbits of storage contains onlym<nbits of information, then that information can in principle be encoded in aboutmbits, at least on the average. This principle is the basis ofdata compressiontechnology. 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 1,300exabytesof hardware digits. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information.When optimally compressed, the resulting carrying capacity approachesShannon informationorinformation entropy.

Bit-based computing

Certainbitwisecomputerprocessorinstructions (such asbit set) operate at the level of manipulating bits rather than manipulating data interpreted as an aggregate of bits.

In the 1980s, whenbitmappedcomputer displays became popular, some computers provided specializedbit block transferinstructions 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 abyteorword,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 themostorleast significant bitdepending on the context.

Other information units

Main article:Units of information

Similar totorqueandenergyin physics;information-theoretic informationand data storage size have the samedimensionalityofunits 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 theshannon(Sh), thenatural unit of information(nat) and thehartley(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 abinitas an arbitrary information unit equivalent to some fixed but unspecified number of bits.

See also

• Binary numeral system
• Bit rateandbaud rate
• Bitstream
• Byte
• Entropy (information theory)
• Fuzzy bit
• Integer (computer science)
• Nibble
• Primitive data type
• P-bit(probabilistic bit)
• Qubit(quantum bit)
• Shannon (unit)
• Ternary numeral system
• Trit(Trinary digit)

External links

• Bit Calculator– a tool providing conversions between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte
• BitXByteConverterArchived2016-04-06 at theWayback Machine– a tool for computing file sizes, storage capacity, and digital information in various units