Prof. Dr. Thorsten Jungmann (last updated 2026-10-04)
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Claude Elwood Shannon (1916–2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor who is known as the ‘father of information theory’. He studied electrical engineering and mathematics at the University of Michigan, where he was introduced to the work of Boole, and graduated in 1936. He received his doctorate in mathematics from the Massachusetts Institute of Technology (MIT) in 1940. During World War II he worked at Bell Labs on fire-control systems and cryptography, and from 1956 to 1978 he was a professor at MIT.
For digital electronics, the work that matters is his master’s thesis ‘A Symbolic Analysis of Relay and Switching Circuits’ (1937). In it Shannon diagrammed switching circuits that could implement the essential operators of Boolean algebra, showed that these circuits could be used to simplify the arrangement of the electromechanical relays in telephone call routing switches, and proved that they could solve all problems that Boolean algebra could solve. The last chapter presents several circuits, among them an adder for binary numbers with a full-adder stage for each digit. Using electrical switches to implement logic is the fundamental concept that underlies all electronic digital computers, and Shannon’s work became the foundation of digital circuit design. The thesis won the Alfred Noble Prize in 1939. The Shannon expansion (German: Shannon-Zerlegung) also bears his name. It expresses a logic function F as the sum of two products: the variable x multiplied by F with x set to 1, plus the complement of x multiplied by F with x set to 0. By repeated application, any logic function can be implemented with a hierarchy of multiplexers. The identity was, however, already presented by Boole in 1854; Shannon wrote it down in 1938, in the published version of his thesis, as the expansion of a function about one variable, with its circuit interpretation, and in the literature of computer design and switching theory it is often incorrectly attributed to him. In the same paper he stated a generalization of De Morgan’s laws that is known as Shannon’s law (German: Shannonscher Satz): the complement of a logic function is obtained by complementing every variable and interchanging AND and OR.
Erratum in the textbook by LaMeres
LaMeres [5, p. 93] states that Shannon applied Boole’s algebraic framework to switching circuits ‘in 1930’ and ‘at Bell Labs’. In fact, he did this work in 1937 in his master’s thesis at MIT, which was published in 1938.
In 1948 Shannon published ‘A Mathematical Theory of Communication’ in the Bell System Technical Journal, in which he developed information entropy as a measure of the information content of a message and thereby essentially founded information theory. In it he used the term bit, crediting the word to John W. Tukey. In 1949 he gave the sampling theorem its widely used form, without claiming to have originated it; the theorem was essential in enabling telecommunications to move from analogue to digital transmission systems. The Shannon–Hartley theorem (German: Shannon-Hartley-Gesetz), which gives the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise, is named after him and Ralph Hartley.
Reference and further reading:
https://en.wikipedia.org/wiki/Claude_Shannon
https://en.wikipedia.org/wiki/Boole%27s_expansion_theorem
https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem
Image source: Wikimedia Commons (CC BY 2.0, Tekniska museet, author unknown)
