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[[File:Binary to Hexadecimal or Decimal.jpg|thumb|Binary to Hexadecimal or Decimal]]
A [[bit string]], interpreted as a binary number, can be [[binary number#Decimal|translated into a decimal number]]. For example, the [[letter case|lower case]] ''a'', if represented by the bit string <code>01100001</code> (as it is in the standard [[ASCII]] code), can also be represented as the decimal number "97".
==History of binary codes==
=== Invention ===
The modern binary number system, the basis for binary code, is an invention by [[Gottfried Leibniz]] in 1689 and appears in his article ''Explication de l'Arithmétique Binaire (''English: ''Explanation of the Binary Arithmetic'') which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern binary numeral system. Binary numerals were central to Leibniz's intellectual and theological ideas. He believed that binary numbers were symbolic of the Christian idea of ''[[creatio ex nihilo]]'' or creation out of nothing.<ref name="on">{{cite book |author1=Yuen-Ting Lai |url=https://books.google.com/books?id=U9dOmVt81UAC&pg=PA149 |title=Leibniz, Mysticism and Religion |publisher=Springer |year=1998 |isbn=978-0-7923-5223-5 |pages=149–150}}</ref>''<ref name="lnz">Leibniz G., Explication de l'Arithmétique Binaire, Die Mathematische Schriften, ed. C. Gerhardt, Berlin 1879, vol.7, p.223; Engl. transl.[http://www.leibniz-translations.com/binary.htm]</ref>''In Leibniz's view, binary numbers represented a fundamental form of creation, reflecting the simplicity and unity of the divine.''<ref name="lnz" />'' Leibniz was also attempting to find a way to translate logical reasoning into pure mathematics. He viewed the binary system as a means of simplifying complex logical and mathematical processes, believing that it could be used to express all concepts of arithmetic and logic. ''<ref name="lnz" />''
=== Previous Ideas ===
Leibniz explained in his work that he encountered the ''[[I Ching]], by [[Fu Xi]]<ref name="lnz" />'' that dates from 9th Centry BC in China,<ref name="HackerMoore2002">{{cite book |author1=Edward Hacker |url=https://books.google.com/books?id=S5hLpfFiMCQC&pg=PR13 |title=I Ching: An Annotated Bibliography |author2=Steve Moore |author3=Lorraine Patsco |publisher=Routledge |year=2002 |isbn=978-0-415-93969-0 |page=13}}</ref> through French Jesuit [[Joachim Bouvet]] and noted with fascination how its [[hexagram (I Ching)|hexagrams]] correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical visual binary [[mathematics]] he admired.<ref>{{Cite book|last=Aiton|first=Eric J.|title=Leibniz: A Biography|year=1985|publisher=Taylor & Francis|isbn=978-0-85274-470-3|pages=245–8}}</ref><ref name="smith" /> Leibniz saw the hexagrams as an affirmation of the universality of his own religious belief.<ref name="smith">{{cite book|author1=J.E.H. Smith|title=Leibniz: What Kind of Rationalist?: What Kind of Rationalist?|url=https://books.google.com/books?id=Da_oP3sJs1oC&pg=PA4153|year=2008|publisher=Springer|isbn=978-1-4020-8668-7|page=415}}</ref> After Leibniz ideas were ignored, 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.<ref name="Gottfried Leibniz">{{Cite web|url=http://www.kerryr.net/pioneers/leibniz.htm|title=Gottfried Wilhelm Leibniz (1646 - 1716)|website=www.kerryr.net}}</ref> The binary system of the ''I Ching'' is based on the duality of [[yin and yang]].<ref name="scientific">{{cite book|author1=Jonathan Shectman|title=Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 18th Century|url=https://books.google.com/books?id=SsbChdIiflsC&pg=PA29|year=2003|publisher=Greenwood Publishing|isbn=978-0-313-32015-6|page=29}}</ref> [[Slit drum]]s with binary tones are used to encode messages across Africa and Asia.<ref name="scientific" /> The Indian scholar [[Pingala]] (around 5th–2nd centuries BC) developed a binary system for describing [[prosody (poetry)|prosody]] in his ''Chandashutram''.<ref>{{Cite book|last1=Sanchez|first1=Julio|last2=Canton|first2=Maria P.|title=Microcontroller programming: the microchip PIC|year=2007|publisher=CRC Press|___location=Boca Raton, Florida|isbn=978-0-8493-7189-9|page=37}}</ref><ref>W. S. Anglin and J. Lambek, ''The Heritage of Thales'', Springer, 1995, {{ISBN|0-387-94544-X}}</ref>
[[Mangareva]] people in [[French Polynesia]] were using a hybrid binary-[[decimal]] system before 1450.<ref>{{Cite journal |last1=Bender |first1=Andrea |last2=Beller |first2=Sieghard |date=16 December 2013 |title=Mangarevan invention of binary steps for easier calculation |journal=Proceedings of the National Academy of Sciences |volume=111 |issue=4 |pages=1322–1327 |doi=10.1073/pnas.1309160110 |pmc=3910603 |pmid=24344278 |doi-access=free}}</ref> In the 11th century, scholar and philosopher [[Shao Yong]] developed a method for arranging the hexagrams which corresponds, albeit unintentionally, to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the [[least significant bit]] on top. The ordering is also the [[lexicographical order]] on [[sextuple]]s of elements chosen from a two-element set.<ref>{{cite journal |last=Ryan |first=James A. |date=January 1996 |title=Leibniz' Binary System and Shao Yong's "Yijing" |journal=Philosophy East and West |volume=46 |issue=1 |pages=59–90 |doi=10.2307/1399337 |jstor=1399337}}</ref>
===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" in decimal).
===Binary-coded decimal===
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