Binary Numeral System - History

History

The Indian scholar Pingala (around 5th–2nd centuries BC) developed mathematical concepts for describing prosody, and in doing so 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.

Pingala's Hindu classic titled Chandaḥśāstra (8.23) describes the formation of a matrix in order to give a unique value to each meter. An example of such a matrix is as follows (note that these binary representations are "backwards" compared to modern, Western positional notation):

0 0 0 0 numerical value 1

1 0 0 0 numerical value 2

0 1 0 0 numerical value 3

1 1 0 0 numerical value 4

A set of eight trigrams (Bagua) and a set of 64 hexagrams ("sixty-four" gua), analogous to the three-bit and six-bit binary numerals, were in usage at least as early as the Zhou Dynasty of ancient China through the classic text Yijing.

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 sextuples of elements chosen from a two-element set.

Similar sets of binary combinations have also been used in traditional 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 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. 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". (See Bacon's cipher.)

The modern binary number system was studied by Gottfried Leibniz in 1679. See his article: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 Yijing (or I-Ching) and noted with fascination how its 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 mathematics he admired.

In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. His logical calculus was to become instrumental in the design of digital electronic circuitry.

In 1937, Claude Shannon produced his master's thesis at MIT that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the first time in history. Entitled A Symbolic Analysis of Relay and Switching Circuits, Shannon's thesis essentially founded practical digital circuit design.

In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based computer he dubbed the "Model K" (for "Kitchen", where he had assembled it), which calculated using binary addition. Bell Labs thus authorized a full research programme in late 1938 with Stibitz at the helm. Their Complex Number Computer, completed 8 January 1940, was able to calculate complex numbers. In a demonstration to the American Mathematical Society conference at Dartmouth College on 11 September 1940, Stibitz was able to send the Complex Number Calculator remote commands over telephone lines by a teletype. It was the first computing machine ever used remotely over a phone line. Some participants of the conference who witnessed the demonstration were John Von Neumann, John Mauchly and Norbert Wiener, who wrote about it in his memoirs.