Editing Binary code (section)

=== Previous Ideas ===
Leibniz explained in his work that he encountered the ''[[I Ching]]'' by [[Fu Xi]]<ref name="lnz" /> that dates from the 9th century 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>

[[File:George Boole color.jpg|thumb|upright|[[George Boole]]]]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.<ref name="Bacon1605" /> 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".<ref name="Bacon1605">{{Cite web|last=Bacon|first=Francis|author-link=Francis Bacon|title=The Advancement of Learning|url=http://home.hiwaay.net/~paul/bacon/advancement/book6ch1.html|year=1605|volume=6|location=London|pages=Chapter 1}}</ref>