Unit of information
"Qbit (quettabit)" redirects here. For quantum bits, see
Qubit
.
The
bit
is the most basic
unit of information
in
computing
and digital
communications
. 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 volts and no lower than 2.6 volts, respectively; while TTL inputs are specified to recognize 0.8 volts or below as
0
and 2.2 volts 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.
|
Decimal
|
Value
|
Metric
|
1000
|
kbit
|
kilobit
|
1000
2
|
Mbit
|
megabit
|
1000
3
|
Gbit
|
gigabit
|
1000
4
|
Tbit
|
terabit
|
1000
5
|
Pbit
|
petabit
|
1000
6
|
Ebit
|
exabit
|
1000
7
|
Zbit
|
zettabit
|
1000
8
|
Ybit
|
yottabit
|
1000
9
|
Rbit
|
ronnabit
|
1000
10
|
Qbit
|
quettabit
|
|
Binary
|
Value
|
IEC
|
|
1024
|
Kibit
|
kibibit
|
Kbit
|
Kb
|
kilobit
|
1024
2
|
Mibit
|
mebibit
|
Mbit
|
Mb
|
megabit
|
1024
3
|
Gibit
|
gibibit
|
Gbit
|
Gb
|
gigabit
|
1024
4
|
Tibit
|
tebibit
|
—
|
1024
5
|
Pibit
|
pebibit
|
—
|
1024
6
|
Eibit
|
exbibit
|
—
|
1024
7
|
Zibit
|
zebibit
|
—
|
1024
8
|
Yibit
|
yobibit
|
—
|
—
|
—
|
|
Orders of magnitude of data
|
Multiple bits
[
edit
]
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 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
(10
3
) through
yotta
(10
24
) 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.
Please help update this section to reflect recent events or newly available information.
(
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
]
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
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 Lopez (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
]
Look up
bit
in Wiktionary, the free dictionary.
- Bit Calculator
? a tool providing conversions between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte
- BitXByteConverter
? a tool for computing file sizes, storage capacity, and digital information in various units
|
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Platform-independent units
| |
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Platform-dependent units
| |
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Metric bit units
| |
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Metric byte units
| |
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