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The term digital was first suggested by [[George Stibitz|George Robert Stibitz]] and refers to where a signal, such as a voltage, is not used to directly represent a value (as it would be in an [[analog computer]]), but to encode it. In November 1937, Stibitz, then working at Bell Labs (1930–1941),<ref name=":0">{{cite web |title=Computer Pioneers – George Stibitz |url=https://history.computer.org/pioneers/stibitz.html |website=history.computer.org |access-date=2018-11-08 |archive-date=2018-10-05 |archive-url=https://web.archive.org/web/20181005004432/http://history.computer.org/pioneers/stibitz.html |url-status=live}}</ref> completed a relay-based calculator he later dubbed the "[[Model K (calculator)|Model K]]" (for "'''k'''itchen table", on which he had assembled it), which became the first [[binary adder]].<ref>{{cite book|last=Ritchie |first=David|date=1986|title=The Computer Pioneers|page=[https://archive.org/details/computerpioneers00ritc/page/35 35]|___location=New York|publisher=Simon and Schuster |isbn=067152397X|url=https://archive.org/details/computerpioneers00ritc}}</ref> Typically signals have two states – low (usually representing 0) and high (usually representing 1), but sometimes [[three-valued logic]] is used, especially in high-density memory. Modern computers generally use [[Boolean logic|binary logic]], but many early machines were [[decimal computer]]s. In these machines, the basic unit of data was the decimal digit, encoded in one of several schemes, including [[binary-coded decimal]] or BCD, [[Bi-quinary coded decimal|bi-quinary]], [[excess-3]], and [[two-out-of-five code]].
The mathematical basis of digital computing is [[Boolean algebra]], developed by the British mathematician [[George Boole]] in his work ''[[The Laws of Thought]]'', published in 1854. His Boolean algebra was further refined in the 1860s by [[William Jevons]] and [[Charles Sanders Peirce]], and was first presented systematically by [[Ernst Schröder (mathematician)|Ernst Schröder]] and [[A. N. Whitehead]].<ref name="DunnHardegree2001">{{cite book|first1=J. Michael|last1=Dunn|first2=Gary M.|last2=Hardegree|year=2001 |title=Algebraic methods in philosophical logic |url=https://books.google.com/books?id=-AokWhbILUIC&pg=PA2 |publisher=Oxford University Press US|isbn=978-0-19-853192-0|page=2|access-date=2016-06-04 |archive-date=2023-02-02 |archive-url=https://web.archive.org/web/20230202181643/https://books.google.com/books?id=-AokWhbILUIC&pg=PA2|url-status=live}}</ref> In 1879 Gottlob Frege
In the 1930s and working independently, American [[electronic engineer]] [[Claude Shannon]] and Soviet [[logician]] [[Victor Shestakov]] both showed a [[one-to-one correspondence]] between the concepts of [[Boolean logic]] and certain electrical circuits, now called [[logic gate]]s, which are now ubiquitous in digital computers.{{sfn|Shannon|1938}} They showed that electronic relays and switches can realize the [[expression (mathematics)|expression]]s of [[Boolean algebra (logic)|Boolean algebra]].{{sfn|Shannon|1940}} This thesis essentially founded practical [[digital circuit]] design. In addition Shannon's paper gives a correct circuit diagram for a 4 bit digital binary adder.{{sfn|Shannon|1938|pp=494–495|ps=.{{verify source|date=August 2023|reason=Neither Shannon (1938) of Shannon (1940) include pages 494–495.}}}}
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