25,161
edits
Changes
Bit
,Created page with "'''Home * Programming * Data * Bit''' border|right|thumb|link=http://ljkrakauer.com/LJK/essays/bits.htm| [[PDP-6 Memory#FlipF..."
'''[[Main Page|Home]] * [[Programming]] * [[Data]] * Bit'''
[[FILE:flipflop6as.jpg|border|right|thumb|link=http://ljkrakauer.com/LJK/essays/bits.htm| [[PDP-6]] [[Memory#FlipFlop|flip-flop]] stores one bit <ref>[http://ljkrakauer.com/LJK/essays/bits.htm Bits] by [[Lawrence J. Krakauer]]</ref> ]]
'''Bit''',<br/>
the [https://en.wikipedia.org/wiki/Units_of_information basic unit] of [https://en.wikipedia.org/wiki/Information information] in [https://en.wikipedia.org/wiki/Information_theory information theory] and [https://en.wikipedia.org/wiki/Computing computing] - a binary digit, either 0 or 1 in the arithmetical sense, 'false' or 'true' in the boolean sense, black (dark) or white (light) as a [[Color]] in [[Chess]], etc..
=Quote=
by [[Claude Shannon]] in ''A Mathematical Theory of Communication'' 1948 <ref>[[Claude Shannon]] ('''1948'''). ''A Mathematical Theory of Communication'', [http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf pdf reprint]</ref>:
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 [https://en.wikipedia.org/wiki/John_Tukey J. W. Tukey]. A device with two stable positions, such as a [https://en.wikipedia.org/wiki/Relay relay] or a [[Memory#FlipFlop|flip-flops]] circuit, can store one bit of information.
=Aggregations=
Aggregations of bits are used to code numbers, integers or floating point values, characters, codes and sets. Four bits are called a [[Nibble]] with 16 states - written as one hexadecimal digit <span style="background-color: #d6d6d6;">{'0'..'9', 'A'-'F'}</span>. A group of eight Bits, two Nibbles or one [[Byte]] with 256 states (e.g. unsigned numbers 0..255) is most often the smallest addressable unit in computer architectures. [[Bitboards]] are set-wise bit aggregations which covers all 64 [[Squares|squares]] of a [[Chessboard]].
<span id="BitwiseArithmetic"></span>
=Bitwise Arithmetic=
Bitwise addition (Modulo 2) and subtraction with aggregations of Bits without overflows can be applied by bitwise [[General Setwise Operations#ExclusiveOr|exclusive or]]:
{| class="wikitable"
|-
! a
! b
! a xor b
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | 0
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 1
| style="text-align:center;" | 1
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 0
| style="text-align:center;" | 1
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 0
|}
=See also=
* [[Nibble]]
* [[Byte]]
* [[Word]]
* [[Double Word]]
* [[Quad Word]]
* [[Bitboards]]
* [[BitScan]]
* [[Bit-Twiddling]]
* [[General Setwise Operations]]
: [[General Setwise Operations#TheLeastSignificantOneBitLS1B|Least Significant One Bit]]
: [[General Setwise Operations#TheMostSignificantOneBitMS1B|Most Significant One Bit]]
=External Links=
* [https://en.wikipedia.org/wiki/Bit Bit from Wikipedia]
* [https://en.wikipedia.org/wiki/Bit_%28disambiguation%29 Bit (disambiguation) from Wikipedia]
* [https://en.wikipedia.org/wiki/Nat_%28information%29 Nat (information) from Wikipedia]
* [https://en.wikipedia.org/wiki/Ban_%28information%29 Ban (information) from Wikipedia]
* [https://en.wikipedia.org/wiki/Qubit Qubit from Wikipedia]
* [https://en.wikipedia.org/wiki/Shannon_(unit) shannon (unit) from Wikipedia]
* [http://ljkrakauer.com/LJK/essays/bits.htm Bits] by [[Lawrence J. Krakauer]]
=References=
<references />
'''[[Data|Up one level]]'''
[[FILE:flipflop6as.jpg|border|right|thumb|link=http://ljkrakauer.com/LJK/essays/bits.htm| [[PDP-6]] [[Memory#FlipFlop|flip-flop]] stores one bit <ref>[http://ljkrakauer.com/LJK/essays/bits.htm Bits] by [[Lawrence J. Krakauer]]</ref> ]]
'''Bit''',<br/>
the [https://en.wikipedia.org/wiki/Units_of_information basic unit] of [https://en.wikipedia.org/wiki/Information information] in [https://en.wikipedia.org/wiki/Information_theory information theory] and [https://en.wikipedia.org/wiki/Computing computing] - a binary digit, either 0 or 1 in the arithmetical sense, 'false' or 'true' in the boolean sense, black (dark) or white (light) as a [[Color]] in [[Chess]], etc..
=Quote=
by [[Claude Shannon]] in ''A Mathematical Theory of Communication'' 1948 <ref>[[Claude Shannon]] ('''1948'''). ''A Mathematical Theory of Communication'', [http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf pdf reprint]</ref>:
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 [https://en.wikipedia.org/wiki/John_Tukey J. W. Tukey]. A device with two stable positions, such as a [https://en.wikipedia.org/wiki/Relay relay] or a [[Memory#FlipFlop|flip-flops]] circuit, can store one bit of information.
=Aggregations=
Aggregations of bits are used to code numbers, integers or floating point values, characters, codes and sets. Four bits are called a [[Nibble]] with 16 states - written as one hexadecimal digit <span style="background-color: #d6d6d6;">{'0'..'9', 'A'-'F'}</span>. A group of eight Bits, two Nibbles or one [[Byte]] with 256 states (e.g. unsigned numbers 0..255) is most often the smallest addressable unit in computer architectures. [[Bitboards]] are set-wise bit aggregations which covers all 64 [[Squares|squares]] of a [[Chessboard]].
<span id="BitwiseArithmetic"></span>
=Bitwise Arithmetic=
Bitwise addition (Modulo 2) and subtraction with aggregations of Bits without overflows can be applied by bitwise [[General Setwise Operations#ExclusiveOr|exclusive or]]:
{| class="wikitable"
|-
! a
! b
! a xor b
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | 0
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 1
| style="text-align:center;" | 1
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 0
| style="text-align:center;" | 1
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 0
|}
=See also=
* [[Nibble]]
* [[Byte]]
* [[Word]]
* [[Double Word]]
* [[Quad Word]]
* [[Bitboards]]
* [[BitScan]]
* [[Bit-Twiddling]]
* [[General Setwise Operations]]
: [[General Setwise Operations#TheLeastSignificantOneBitLS1B|Least Significant One Bit]]
: [[General Setwise Operations#TheMostSignificantOneBitMS1B|Most Significant One Bit]]
=External Links=
* [https://en.wikipedia.org/wiki/Bit Bit from Wikipedia]
* [https://en.wikipedia.org/wiki/Bit_%28disambiguation%29 Bit (disambiguation) from Wikipedia]
* [https://en.wikipedia.org/wiki/Nat_%28information%29 Nat (information) from Wikipedia]
* [https://en.wikipedia.org/wiki/Ban_%28information%29 Ban (information) from Wikipedia]
* [https://en.wikipedia.org/wiki/Qubit Qubit from Wikipedia]
* [https://en.wikipedia.org/wiki/Shannon_(unit) shannon (unit) from Wikipedia]
* [http://ljkrakauer.com/LJK/essays/bits.htm Bits] by [[Lawrence J. Krakauer]]
=References=
<references />
'''[[Data|Up one level]]'''
