Bit

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

Fundamental units of information
bit (binary) nat (base e) ban (decimal) qubit (quantum)
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Processors
1-bit	4-bit	8-bit	12-bit	16-bit	18-bit	24-bit	31-bit	32-bit	36-bit	48-bit	60-bit	64-bit	128-bit
Applications
		8-bit		16-bit				32-bit				64-bit
Data Sizes
bit   nibble   octet   byte
halfword   word   dword   qword
IEEE floating-point standard
Single precision floating-point format (32-bit)  Double precision floating-point format (64-bit)  Quadruple precision floating-point format (128-bit)

A bit (a contraction of binary digit) is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one 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, etc.

In computing, a bit can also be defined as a variable or computed quantity that can have only two possible values. These two values are often interpreted as binary digits and are usually denoted by the Arabic numerical digits 0 and 1. The two values can also be interpreted as logical values (true/false, yes/no), algebraic signs (+/−), activation states (on/off), or any other two-valued attribute. The correspondence 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. The length of a binary number may be referred to as its "bit-length."

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 either simply "bit" (recommended by the ISO/IEC standard 80000-13 (2008)) or lowercase "b" (recommended by the IEEE 1541 Standard (2002)).

History

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 Semen Korsakov, Charles Babbage, Hermann Hollerith, and early computer manufacturers like IBM. Another variant of that idea was the perforated paper tape. In all those systems, the medium (card or tape) conceptually carried an array of hole positions; each position could be either punched through or not, thus potentially 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.^[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 punched cards used in the mechanical computers of that time.^[4] The first programmable computer built by Konrad Zuse used binary notation for numbers.

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 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. The same principle was later used in the magnetic bubble memory developed in the 1980s, and is still found in various magnetic strip items such as metro tickets and some credit cards.

In modern semiconductor memory, such as dynamic random access memory or flash memory, the two values of a bit may be represented by two levels of electric charge stored in a capacitor. In programmable logic arrays and certain types of 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.

Information capacity and information compression

When the information capacity of a storage system or a communication channel is presented in bits or bits per second, this often refers to binary digits, which is a hardware capacity to store binary code (0 or 1, up or down, current or not, etc). Information capacity of a storage system is only an upper bound to the actual quantity of information stored therein. If the two possible values of one 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 entropic bits, because no resolution of uncertainty and therefore no information). 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 in 2007. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information^[5]. When optimally compressed, the resulting carrying capacity approaches Shannon information or information entropy.

Multiple bits

v · d · e Multiples of bits
SI decimal prefixes		IEC binary prefixes
Name (Symbol)	Value	Name (Symbol)	Value
kilobit (kbit)	103	kibibit (Kibit)	210 = 1.024 × 103
megabit (Mbit)	106	mebibit (Mibit)	220 ≈ 1.049 × 106
gigabit (Gbit)	109	gibibit (Gibit)	230 ≈ 1.074 × 109
terabit (Tbit)	1012	tebibit (Tibit)	240 ≈ 1.100 × 1012
petabit (Pbit)	1015	pebibit (Pibit)	250 ≈ 1.126 × 1015
exabit (Ebit)	1018	exbibit (Eibit)	260 ≈ 1.153 × 1018
zettabit (Zbit)	1021	zebibit (Zibit)	270 ≈ 1.181 × 1021
yottabit (Ybit)	1024	yobibit (Yibit)	280 ≈ 1.209 × 1024
See also: Nibble · Byte · Multiples of bytes Orders of magnitude of data

There are several units of information which are defined as multiples of bits, such as byte (8 bits), kilobit (either 1000 or 2¹⁰ = 1024 bits), megabyte (either 8000000 or 8×2²⁰ = 8388608bits), etc.

Computers usually manipulate bits in groups of a fixed size, conventionally named "words". The number of bits in a word varies with the computer model; typically between 8 to 80 bits; or even more in some specialized machines.

The International Electrotechnical Commission's standard IEC 60027 specifies that the symbol for binary digit should be "bit", and this should be used in all multiples, such as "kbit" (for kilobit).^[6] However, the letter "b" (in lower case) is widely used too. The letter "B" (upper case) is both the standard and customary symbol for byte.

In telecommunications (including computer networks), data transfer rates are usually measured in bits per second (bit/s) or its multiples, such as kbit/s. (This unit is not to be confused with baud.)

A millibit is a (rare) unit of information equal to one thousandth of a bit.^[7]

Bit-based computing

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 ("bitblt" or "blit") instructions to set or copy the bits that corresponded to a given rectangular area on the screen.

In most computers and programming languages, when a bit within a group of bits such as a byte or word is 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.

Other information units

Main article: Units of information

Other units of information, sometimes used in information theory, include the natural digit also called a nat or nit and defined as log₂ e (≈ 1.443) bits, where e is the base of the natural logarithms; and the dit, 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

• Byte
• Integer (computer science)
• Primitive data type
• Bitstream
• Entropy (information theory)
• Binary numeral system
• Ternary numeral system
• Bit (Tron character)

References

1. ^ John B. Anderson, Rolf Johnnesson (2006) Understanding Information Transmission.
2. ^ Simon Haykin (2006), Digital Communications
3. ^ ^{a b} Norman Abramson (1963), Information theory and coding. McGraw-Hill.
4. ^ Vannevar Bush, Instrumental Analysis, Bull. Amer. Math. Soc., vol. 42, no. 10, pp. 649-669, 1936.
5. ^ "The World’s Technological Capacity to Store, Communicate, and Compute Information", especially Supporting online material, Martin Hilbert and Priscila López (2011), Science (journal), 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html
6. ^ National Institute of Standards and Technology (2008), Guide for the Use of the International System of Units. Online version.
7. ^ "The textural language machine: a system of associative electronicnetworks for efficient processing of neural language texts". Hilberg, W. Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences, 1991. Volume i, Issue , 8-11 Jan 1991 Page(s):219 - 228 vol.1.[1]
8. ^ Amitabha Bhattacharya, Digital Communication

External links

• Bit Calculator - Convert between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte