Editing Binary number (section)

===Western predecessors to Leibniz===
In the late 13th century [[Ramon Llull]] had the ambition to account for all wisdom in every branch of human knowledge of the time. For that purpose he developed a general method or "Ars generalis" based on binary combinations of a number of simple basic principles or categories, for which he has been considered a predecessor of computing science and artificial intelligence.<ref>(see Bonner 2007 [http://lullianarts.net/] {{Webarchive|url=https://web.archive.org/web/20140403194204/http://lullianarts.net/|date=3 April 2014}}, Fidora et al. 2011 [https://www.iiia.csic.es/es/publications/ramon-llull-ars-magna-artificial-intelligence/] {{Webarchive|url=https://web.archive.org/web/20190408011909/https://www.iiia.csic.es/es/publications/ramon-llull-ars-magna-artificial-intelligence/|date=8 April 2019}})</ref>

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> (See [[Bacon's cipher]].)

In 1617, [[John Napier]] described a system he called [[location arithmetic]] for doing binary calculations using a non-positional representation by letters.
[[Thomas Harriot]] investigated several positional numbering systems, including binary, but did not publish his results; they were found later among his papers.<ref>{{cite journal|last=Shirley|first=John W.|title=Binary numeration before Leibniz|journal=American Journal of Physics|volume=19|year=1951|issue=8|pages=452–454|doi=10.1119/1.1933042|bibcode=1951AmJPh..19..452S}}</ref>
Possibly the first publication of the system in Europe was by [[Juan Caramuel y Lobkowitz]], in 1700.<ref>{{cite journal|last=Ineichen|first=R.|title=Leibniz, Caramuel, Harriot und das Dualsystem|language=de|journal=Mitteilungen der deutschen Mathematiker-Vereinigung|volume=16|year=2008|issue=1|pages=12–15|doi=10.1515/dmvm-2008-0009|s2cid=179000299|url=http://page.math.tu-berlin.de/~mdmv/archive/16/mdmv-16-1-12-ineichen.pdf}}</ref>