The Indian scholar Pingala (circa 5th–2nd centuries BC) developed mathematical concepts for describing prosody, and in so doing presented the first known description of a binary numeral system.He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code.
A set of eight trigrams and a set of 64hexagrams, analogous to the three-bit and six-bit binary numerals, were known in ancient China through the classic text I Ching. In the 11th century, scholar and philosopher Shao Yong developed a methodfor arranging the hexagrams which corresponds to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the least significant bit on top. There is, however, no evidence that Shaounderstood binary computation. The ordering is also the lexicographical order on sextuples of elements chosen from a two-element set.
Similar sets of binary combinations have also been used intraditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been widely applied in sub-Saharan Africa.
In 1605 FrancisBacon 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.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, byTrumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature". (See Bacon's cipher.)
The modern binary number system was fully documented by Gottfried Leibniz in hisarticle Explication de l'Arithmétique Binaire(1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. As a Sinophile, Leibniz was aware of the I Ching and noted with...
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