Binary code
A binary code represents
In computing and telecommunications, binary codes are used for various methods of
A
01100001
(as it is in the standard ASCIIHistory of binary codes
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The modern binary number system, the basis for binary code, was invented by
Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing.[4] Leibniz was trying to find a system that converts logic verbal statements into a pure mathematical one[citation needed]. After his ideas were ignored, he came across a classic Chinese text called I Ching or 'Book of Changes', which used 64 hexagrams of six-bit visual binary code. The book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones. During this time period, Leibniz had not yet found a use for this system.[5]
Binary systems predating Leibniz also existed in the ancient world. The aforementioned I Ching that Leibniz encountered dates from the 9th century BC in China.
The residents of the island of
In 1605 Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text.[12] Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature".[12]
Other forms of binary code
This section possibly contains original research. (March 2015) |
The bit string is not the only type of binary code: in fact, a binary system in general, is any system that allows only two choices such as a switch in an electronic system or a simple true or false test.
Braille
Braille is a type of binary code that is widely used by the blind to read and write by touch, named for its creator, Louis Braille. This system consists of grids of six dots each, three per column, in which each dot has two states: raised or not raised. The different combinations of raised and flattened dots are capable of representing all letters, numbers, and punctuation signs.
Bagua
The
Ifá, Ilm Al-Raml and Geomancy
The Ifá/Ifé system of divination in African religions, such as of Yoruba, Igbo, and Ewe, consists of an elaborate traditional ceremony producing 256 oracles made up by 16 symbols with 256 = 16 x 16. An initiated priest, or Babalawo, who had memorized oracles, would request sacrifice from consulting clients and make prayers. Then, divination nuts or a pair of chains are used to produce random binary numbers,[16] which are drawn with sandy material on an "Opun" figured wooden tray representing the totality of fate.
Through the spread of
This was thought to be another possible route from which computer science was inspired,[17] as Geomancy arrived at Europe at an earlier stage (about 12th Century, described by Hugh of Santalla) than I Ching (17th Century, described by Gottfried Wilhelm Leibniz).
Coding systems
ASCII code
The
1100001
as a bit string (which is "97" in decimal).
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.[18]
Early uses of binary codes
- 1875: Émile Baudot "Addition of binary strings in his ciphering system," which, eventually, led to the ASCII of today.
- 1884: The Linotype machine where the matrices are sorted to their corresponding channels after use by a binary-coded slide rail.
- 1932: C. E. Wynn-Williams "Scale of Two" counter[19]
- 1937: Alan Turing electro-mechanical binary multiplier
- 1937: "excess three" code in the Complex Computer[19]
- 1937: Atanasoff–Berry Computer[19]
- 1938: Konrad Zuse Z1
Current uses of binary
Most modern computers use binary encoding for instructions and data.
Weight of binary codes
The weight of a binary code, as defined in the table of constant-weight codes,[20] is the Hamming weight of the binary words coding for the represented words or sequences.
See also
References
- ^ Leibniz G., Explication de l'Arithmétique Binaire, Die Mathematische Schriften, ed. C. Gerhardt, Berlin 1879, vol.7, p.223; Engl. transl.[1]
- ISBN 978-0-85274-470-3.
- ^ ISBN 978-1-4020-8668-7.
- ISBN 978-0-7923-5223-5.
- ^ "Gottfried Wilhelm Leibniz (1646 - 1716)". www.kerryr.net.
- ISBN 978-0-415-93969-0.
- ^ ISBN 978-0-313-32015-6.
- ISBN 978-0-8493-7189-9.
- ISBN 0-387-94544-X
- PMID 24344278.
- JSTOR 1399337.
- ^ a b Bacon, Francis (1605). "The Advancement of Learning". London. pp. Chapter 1.
- ^ "What's So Logical About Boolean Algebra?". www.kerryr.net.
- ^ "Claude Shannon (1916 - 2001)". www.kerryr.net.
- ISBN 978-0-691-09750-3.
- OCLC 839396781.
- ^ Eglash, Ron (June 2007). "The fractals at the heart of African designs". www.ted.com. Archived from the original on 2021-07-27. Retrieved 2021-04-15.
- Cowlishaw, Mike F. (2015) [1981, 2008]. "General Decimal Arithmetic". IBM. Retrieved 2016-01-02.
- ^ a b c Glaser 1971
- ^ Table of Constant Weight Binary Codes
External links
- Sir Francis Bacon's BiLiteral Cypher system Archived 2016-09-23 at the Wayback Machine, predates binary number system.
- Weisstein, Eric W. "Error-Correcting Code". MathWorld.
- Table of general binary codes. An updated version of the tables of bounds for small general binary codes given in M.R. Best; A.E. Brouwer; F.J. MacWilliams; A.M. Odlyzko; N.J.A. Sloane (1978), "Bounds for Binary Codes of Length Less than 25", IEEE Trans. Inf. Theory, 24: 81–93, .
- Table of Nonlinear Binary Codes. Maintained by Simon Litsyn, E. M. Rains, and N. J. A. Sloane. Updated until 1999.
- Glaser, Anton (1971). "Chapter VII Applications to Computers". History of Binary and other Nondecimal Numeration. Tomash. ISBN 978-0-938228-00-4. cites some pre-ENIAC milestones.
- First book in the world fully written in binary code: (IT) Luigi Usai, 01010011 01100101 01100111 01110010 01100101 01110100 01101001, Independently published, 2023, ISBN 979-8-8604-3980-1. URL consulted September 8, 2023.