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Bit

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For other uses, see the unit of information.

A bit is a binary digit, 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 storage and communication in digital computing and digital information theory. Information theory also often uses the natural digit, called either a nit or a nat. Quantum computing uses qubits; single piece of quantum information encoded on a two level quantum system and hence having the potential to exist in superposition of "true" and "false".

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.

Binary digit

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 cards used in the mechanical computers of that time. [1]

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 states from each other. Gregory Bateson defined a bit as "a difference which makes a difference".[2]

Representation

Transmission

Bits can be implemented in many forms depending on the requirements in an application context. For example, in digital circuitry in most computing devices as well as flash memories, a bit is an electrical 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 volts (in the case of TTL circuitry), while a logical 0 (false value or low) is represented by 0 volts.

Storage

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 discs or stored in non-volatile flash memory.

Unit

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[citation needed], 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 nats (ln(2)), or 0.301 hartleys (log10(2)).

Consider, for example, a computer file with one thousand 0s and 1s which can be 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.[citation needed] However, most of the time, the meaning is clear from the context.

Abbreviation and symbol

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.

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."[3]

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.[4]

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

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.

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.[5] 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)

See also

References

  1. ^ Darwin among the machines: the evolution of global intelligence, George Dyson, 1997. ISBN 0-201-40649-7
  2. ^ Social Systems
  3. ^ http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31898
  4. ^ http://physics.nist.gov/cuu/pdf/sp811.pdf
  5. ^ nybble reference.com sourced from Jargon File 4.2.0, accessed 2007-08-12
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