Bit

One bit of information equal to 0 (zero)
the lamp is off

One bit of information equal to 1 (unit)
the lamp is on

Uppercase Cyrillic letter " M " encoded in ISO 8859-5 encoded in 8 bits
$10111100$ ${\ displaystyle 10111100}$ ${\ displaystyle 10111100}$

Bit (Russian designation: bit ; international: bit ; from the English bi nary digi t - binary number ; also puns : English bit - a piece, a particle) - a unit of measurement of the amount of information . 1 bit of information - a symbol or signal that can take two values: on or off, yes or no, high or low, charged or uncharged; in binary, it is 1 (unit) or 0 (zero).

In the Russian Federation , bit designations, as well as the rules for its use and spelling, are established by the Regulation on units of quantities allowed for use. In accordance with this provision, the bit belongs to the number of off-system units with the scope of “information technology, communication” and unlimited validity ^[1] . Previously, bit designations were also established in GOST 8.417-2002 ^[2] . For the formation of multiple units, it is used with SI prefixes and with binary prefixes .

Content

History

In 1703, in the Explanation of Binary Arithmetic ^[3], Leibniz writes that the binary number system was described by a Chinese king (emperor) and a philosopher named Fu Xi , who lived more than 4000 years before Leibniz. Brief Modern Anglo-Saxon ^{[ clarify ] the} names of Chinese Liangyi ( yin-yang ("0" - "1"), Chinese binary digit , Chinese bit) at that time did not yet have. The Chinese two - bit - “ sy-xiang ”, forming four digrams , and the Chinese tribit - “ ba-gua ”, forming eight pre-celestial and post-celestial trigrams , in modern Anglo-Saxon ^{[ clarify ] the} terminology of proper names still do not have.
In 1948, Claude Shannon first used the word “ bit ” to refer to the smallest unit of information in the article “ Mathematical Theory of Communication ”. He attributed the origin of this word to John Tukey , who used the abbreviation “bit” instead of the words “binary digit” in Bell's note on January 9, 1947.

Definitions and properties

For three traffic light states, it is necessary

\lceil \log _{2}3\rceil =

{\ displaystyle \ lceil \ log _ {2} 3 \ rceil =}

\lceil 1{,}5849\rceil =

{\ displaystyle \ lceil 1 {,} 5849 \ rceil =}

2 bits of information.
00 - red
01 - yellow
10 - green

Depending on the field of application ( mathematics , electronics , digital technology , computer engineering , information theory , etc.), a bit can be determined in the following ways:

1. In math :

1.1. A bit is one bit of a binary code ( binary digit ). It can take only two mutually exclusive values : “yes” or “no”, “1” or “0”, “on” or “off”, etc.

1.2. Corresponds to one numeric digit in the binary number system , taking the value “0” or “1” (“false” or “true”) ^[4] .

2. In electronics , in digital technology and in computer technology :

2.1. One bit (one binary bit) corresponds to one binary trigger (a trigger having two mutually exclusive possible stable states) or one bit of binary memory .

To go from the number of possible states (possible values) to the number of bits, you can use the formula

\log _{2}(m

{\ displaystyle \ log _ {2} (m}

[possible conditions]

)

{\ displaystyle)}

=n

{\ displaystyle = n}

[bits].

Therefore, for one binary digit ( trigger )

one

{\ displaystyle 1}

[bit]

=\log _{2}(2

{\ displaystyle = \ log _ {2} (2}

[possible conditions]

)

{\ displaystyle)}

.

To go from the number of bits to the number of possible states (possible values), you can use the formula

m

{\ displaystyle m}

[possible conditions]

=2^{n}

{\ displaystyle = 2 ^ {n}}

^[bits] .

2.2. Hartley formula

I=\log _{2}N=n\log _{2}m,

{\ displaystyle I = \ log _ {2} N = n \ log _ {2} m,}

Where

I

{\ displaystyle I}

- amount of information , bits;

N=m^{n}

{\ displaystyle N = m ^ {n}}

- the possible number of different messages (the number of possible states of the n- bit register ), pcs;

m

{\ displaystyle m}

- the number of letters in the alphabet (the number of possible states of one category ( trigger ) of the register in the binary system is 2 ("0" and "1")), pcs;

n

{\ displaystyle n}

- the number of letters in the message (the number of bits (triggers) in the register), pcs.

It is used to measure the volume of storage devices and the volume of digital data.

3. In information theory :

3.1. Bit - the basic unit of measurement of the amount of information equal to the amount of information contained in the experiment, which has two equally probable outcomes; see informational entropy . This is identical to the amount of information in the answer to a question that allows the answer “yes” or “no” and no other (that is, such a quantity of information that allows you to unequivocally answer the question).

3.2. One bit is equal to the amount of information obtained as a result of one of two equally probable events ^[5] .

3.3. Bit - the binary logarithm of probability of equally probable events or the sum of products of probability and the binary logarithm of probability with equally probable events; see informational entropy .

It is used to measure informational entropy . It differs from a bit for measuring storage volumes and volumes of digital data, since a large data volume can have very small information entropy, that is, it can be almost empty entropy.

Physical implementations

In digital technology, a bit (one binary bit ) is implemented by a trigger or one binary bit of memory .

Two physical (in particular electronic) realizations of a bit (one binary bit) are possible:

single-phase (“single-wire”) bit (binary bit). A single binary trigger output is used. A zero level indicates either a logical “0” signal or a circuit malfunction. A high level indicates either a logical “1” signal or a good circuit. Cheaper than a two-phase implementation, but less reliable;
two-phase (paraphase, "two-wire") bit (binary bit). Both outputs of the binary trigger are used. With a working circuit, one of the two levels is high, the other is low. A circuit failure is recognized either by a high level on both wires (on both phases) or a low level on both wires (on both phases). More expensive than single-phase implementation, but more reliable.

In computer technology and data transmission networks, the values “0” and “1” are usually transmitted by different levels of either voltage or current . For example, in microcircuits based on transistor-transistor logic, the value “0” is represented by a voltage in the range from +0 to +0.8 V , and the value “1” is represented by a voltage in the range from +2.4 to +5.0 V.

Conventions

In computer technology, especially in documentation and standards, the word “ bit ” is often used in the meaning of “ binary bit ”. For example: the most significant bit is the most significant bit of a byte or word .

The use of the capital letter “B” to designate a byte meets the requirements of GOST and avoids confusion between abbreviations from “bytes” and “bits”. However, it should be borne in mind that there is no abbreviation for “bits” in the standard, therefore the use of the “GB” record as a synonym for “Gbit” is incorrect.

In the international standard IEC (IEC) 60027-2 2005 ^[6] for use in the electrical and electronic fields, the following notations are recommended:

“Bit” to indicate a bit;
“O” or “B” to indicate an octet or byte. “O” is the only designation in French.

The analogue of a bit in quantum computers is qubit (q-bit; "q" from the English quantum , quantum ).

Binary Logarithms of Other Foundations

Units of information. Designations:

green strokes on the vertical scale on the left are the values of the natural logarithm for integers;
the yellow curve is a graph of the natural logarithm ;
the bit is shown in black and white rectangles, as it takes one of two possible values;
the height of the rectangle of one bit is equal to log _e (2);
“Nibble” - tetrad or nibble , 4 bits ;
trit is shown by three multi-colored rectangles, as it takes one of three possible values;
the height of the rectangle of one trit is equal to log _e (3);
the hart (dit, decit) is shown by a rectangle filled with a gradient; it takes one of 10 possible values;
the height of the rectangle of one hart (dita, decite) is equal to log _e (10); the number of blue strokes is 20; the distance between the strokes is log _e (10) / 20;
the width of the rectangles is 1;
the horizontal line labeled “ 1 Nat ” has a height of 1 nat = log ₂ e .

Replacing the logarithm number from 2 to e , 3 , 4 , 8 , 10 , 16 , 27 , etc., leads, respectively, to the bit (binary) equivalents of rarely used units of nat , trit , tetrite ( tetrit - tetr al dig it ) (two-bit), octit ( octit - oct al dig it ) (tribit), hart (dit ( dit - d ecimal dig it ), ban, decite ( decit - dec imal dig it )), nibble (hexadecite, four-bit), heptacositis, etc., equal respectively:

1\ {\text{nat}}=\log _{2}e=1,44...

{\ displaystyle 1 \ {\ text {nat}} = \ log _ {2} e = 1.44 ...}

bits

1\ {\text{trit}}=\log _{2}3=1,58...

{\ displaystyle 1 \ {\ text {trit}} = \ log _ {2} 3 = 1.58 ...}

bits

1 two-bit =

1\ {\text{tetrit}}=\log _{2}4=2

{\ displaystyle 1 \ {\ text {tetrit}} = \ log _ {2} 4 = 2}

bits

1 tribit =

1\ {\text{octit}}=\log _{2}8=3

{\ displaystyle 1 \ {\ text {octit}} = \ log _ {2} 8 = 3}

bits

1\ {\text{hart}}\ ({\text{dit, ban, decit}})=\log _{2}10=3,32...

{\ displaystyle 1 \ {\ text {hart}} \ ({\ text {dit, ban, decit}}) = \ log _ {2} 10 = 3.32 ...}

bits

1 four-bit =

1\ {\text{nibble}}\ ({\text{hexadecit}})=\log _{2}16=4

{\ displaystyle 1 \ {\ text {nibble}} \ ({\ text {hexadecit}}) = \ log _ {2} 16 = 4}

bits

1\ {\text{heptacosait}}=\log _{2}27=4,75...

{\ displaystyle 1 \ {\ text {heptacosait}} = \ log _ {2} 27 = 4.75 ...}

bit.

Notes

↑ Regulation on units allowed for use in the Russian Federation. Approved by Decree of the Government of the Russian Federation of October 31, 2009 No. 879 Archival copy of November 2, 2013 on the Wayback Machine .
↑ GOST 8.417-2002. Units of quantities. Appendix A (informative) Archived November 8, 2015 on the Wayback Machine .
↑ Leibniz. EXPLANATION OF BINARY ARITHMETIC .
↑ Bit (unopened) . Big Russian Encyclopedia . Date of treatment August 26, 2016.
↑ Dengub V.M., Smirnov V.G. Units of quantities. Reference dictionary. - M .: Publishing house of standards, 1990. - S. 25. - 240 p. - ISBN 5-7050-0118-5 .
↑ Standard fr. "Norme internationale CEI 60027-2", troisième édition or Eng. "International standard IEC 60027-2", third edition from 2005.08, p. 5, 112-117.

[Положение-1] Regulation on units allowed for use in the Russian Federation. Approved by Decree of the Government of the Russian Federation of October 31, 2009 No. 879 Archival copy of November 2, 2013 on the Wayback Machine .

[ГОСТ-2] GOST 8.417-2002. Units of quantities. Appendix A (informative) Archived November 8, 2015 on the Wayback Machine .

[3] Leibniz. EXPLANATION OF BINARY ARITHMETIC .

[4] Bit (unopened) . Big Russian Encyclopedia . Date of treatment August 26, 2016.

[5] Dengub V.M., Smirnov V.G. Units of quantities. Reference dictionary. - M .: Publishing house of standards, 1990. - S. 25. - 240 p. - ISBN 5-7050-0118-5 .

[6] Standard fr. "Norme internationale CEI 60027-2", troisième édition or Eng. "International standard IEC 60027-2", third edition from 2005.08, p. 5, 112-117.

Bit

Content

History

Definitions and properties

Physical implementations

Conventions

Binary Logarithms of Other Foundations

See also

Notes

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