Binary code: Difference between revisions

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[[Image:Wikipedia in binary.gif|thumb |The ASCII-encoded letters of "Wikipedia" represented as binary codes.]]

[[Image:Binary to Hexadecimal or Decimal.jpg|thumb |Values represented in binary, hex and decimal]]

A '''binary code''' is the value of a [[data encoding |data-encoding]] convention represented in a [[Binary number |binary]] notation that usually is a sequence of 0s and 1s; sometimes called a ''[[bit]] string''. For example, [[ASCII]] is an 8-bit text encoding that in addition to the [[human readable]] form (letters) can be represented as binary. ''Binary code'' can also refer to the [[mass noun]] ''code'' asthat ais categorizationnot ofhuman readable in nature such as [[machine code]] and [[bytecode]].

Even though all modern computer data is binary in nature, and therefore, can be represented as binary, other [[numerical base]]s are usually used. [[Power of 2]] bases (including [[hexadecimal |hex]] and [[octal]]) are sometimes considered binary code since their power-of-2 nature makes them inherently linked to binary. [[Decimal]] is, of course, a commonly used representation. For example, ASCII characters are often represented as either decimal or hex. Some types of data such as [[image]] data is sometimes represented as hex, but rarely as decimal.

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; Bagua {{anchor|BaGua}}: The ''[[bagua]]'' is a set of diagrams used in ''[[feng shui]],'' [[Taoist]] [[cosmology]] and ''[[I Ching]]'' studies. The ''ba gua'' consists of 8 trigrams; each a combination of three lines (''yáo'') that are either broken ([[Yin and yang|''yin'']]) or unbroken (''yang'').<ref name='wilhelm'>{{cite book |last=Wilhelm |first=Richard |author-link=Richard Wilhelm (sinologist) |others=trans. by [[Cary F. Baynes]], foreword by [[C. G. Jung]], preface to 3rd ed. by [[Hellmut Wilhelm]] (1967) |title=The I Ching or Book of Changes |publisher=Princeton University Press |year=1950 |___location=Princeton, NJ |url=https://books.google.com/books?id=bbU9AAAAIAAJ&pg=PA266 |isbn=978-0-691-09750-3 |pages=266, 269}}</ref>

; Ifá, Ilm Al-Raml and Geomancy{{anchor|Ifá}}: The [[Ifá]]/Ifé system of divination in African religions, such as of [[Yoruba people |Yoruba]], [[Igbo people |Igbo]], and [[Ewe people |Ewe]], consists of an elaborate traditional ceremony producing 256 oracles made up by 16 symbols with 256 = 16 x 16. A priest, or [[Babalawo]], requests sacrifice from consulting clients and makes prayers. Then, divination [[nut (fruit)|nuts]] or a pair of [[chain]]s are used to produce random binary numbers,<ref>{{Cite book |last=Olupona |first=Jacob K. |title=African Religions: A Very Short Introduction |publisher=[[Oxford University Press]] |year=2014 |isbn=978-0-19-979058-6 |___location=Oxford |pages=45 |oclc=839396781}}</ref> which are drawn with sandy material on an "Opun" figured wooden tray representing the totality of fate.<ref>{{Cite web|last=Eglash|first=Ron|date=June 2007|title=The fractals at the heart of African designs|url=https://www.ted.com/talks/ron_eglash_the_fractals_at_the_heart_of_african_designs/up-next#t-13472|url-status=live|access-date=2021-04-15|website=www.ted.com|archive-url=https://web.archive.org/web/20210727161435/https://www.ted.com/talks/ron_eglash_the_fractals_at_the_heart_of_african_designs/up-next |archive-date=2021-07-27 }}</ref>

==Coding systemsEncoding==

[[File:2D Binary Index.svg|thumb|An example of a recursive [[binary space partitioning]] [[quadtree]] for a 2D index]]

Innumerable encoding systems exists. Some notable examples are described here.

; ASCII: The [[American Standard Code for Information Interchange]] (ASCII) character encoding, is a 7-bit convention for representing (normal/printing) characters and [[Control character |control]] operations. Each printing and control character is assigned a number from 0 to 127. For example, "a" is represented by decimal code 97 which is rendered as bit string <code>1100001</code>.

===ASCII code===

The [[American Standard Code for Information Interchange]] (ASCII), uses a 7-bit binary code to represent text and other characters within computers, communications equipment, and other devices. Each letter or symbol is assigned a number from 0 to 127. For example, lowercase "a" is represented by <code>1100001</code> as a bit string (which is decimal 97).

BCD; arithmeticBinary-coded decimal: [[Binary-coded decimal]] (BCD) is sometimesan preferredencoding toof integer values that consists of a floating4-pointbit numeric[[nibble]] formatsfor ineach commercialdecimal anddigit. financialAs applicationsa wheredecimal thedigit complexis roundingonly behaviors1 of floating-point10 numbersvalues (0 to 9) but 4 bits can encode up to 16 values, and BCD element is inappropriateinvalid for a value greater than 9.<ref name="Cowlishaw_GDA">{{cite web |first=Mike F. |last=Cowlishaw |author-link=Mike F. Cowlishaw |title=General Decimal Arithmetic |orig-year=1981, 2008 |publisher=IBM |date=2015 |url=http://speleotrove.com/decimal/<!-- http://www2.hursley.ibm.com/decimal/ --> |access-date=2016-01-02}}</ref>

===Binary-coded decimal===

[[Binary-coded decimal]] (BCD) is a binary encoded representation of integer values that uses a 4-bit [[nibble]] to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine. The remaining six values are illegal and may cause either a machine exception or unspecified behavior, depending on the computer implementation of BCD arithmetic.

BCD arithmetic is sometimes preferred to floating-point numeric formats in commercial and financial applications where the complex rounding behaviors of floating-point numbers is inappropriate.<ref name="Cowlishaw_GDA">{{cite web |first=Mike F. |last=Cowlishaw |author-link=Mike F. Cowlishaw |title=General Decimal Arithmetic |orig-year=1981, 2008 |publisher=IBM |date=2015 |url=http://speleotrove.com/decimal/<!-- http://www2.hursley.ibm.com/decimal/ --> |access-date=2016-01-02}}</ref>

==See also==