## The Synthesis of Two-Terminal Switching Circuits in The Bell System Technical Journal, Volume XXVIII [28], No.1, pp.59-98, January 1949

New York: American Telephone and Telegraph Company, 1949. 1st Edition. FIRST EDITION IN ORIGINAL WRAPS OF CLAUDE SHANNON’S FOLLOW UP TO HIS SEMINAL MASTER’S THESIS “frequently called the most important master's thesis of the twentieth century with respect to the influence it had on the development of the electronic and computer industries…[and] probably the most significant theoretical step toward the construction of electronic digital computers made prior to World War II” (Origins of Cyberspace 363). In the paper offered, Shannon continued his work using Boolean algebra to synthesize and simplify relay switching circuits, and further, demonstrating that “symmetric Boolean functions may be realized with considerably fewer components than most functions” (Introduction to Logic Design, 181). Known as the Shannon theorem on symmetric functions “Shannon proposes methods for synthesizing switching circuits according to their function to achieve the minimum number of switches for a given task. The theorems and methods he introduced have found modern applications in the design of computer logic circuits and chips” (Nelson, Journal of Symbolic Logic, Vol. 20, p. 69).

“In his thesis, Shannon recognized that the true/false values in Boole's two-valued logic were analogous to the open and closed states of electrical circuits. From this it followed that Boolean algebra could be used to describe or to design electrical circuits. Because Boolean algebra, invented by George Boole…makes it possible to devise a procedure or build a device, the state of which can store specific information, once Shannon showed that electrical circuitry can perform logical and mathematical operations, and can also store the result of these operations, the inference could be drawn that it was possible to design calculating machines using electrical switches.

“When Shannon wrote his thesis he was thinking of electro-mechanical relays used as switches in telephone technology rather than vacuum tubes that would be used in electronic computers because of their higher speed. But of course the same principles applied to both technologies” (ibid). In this paper, Shannon extends the ideas and methods presented in his thesis. One of his goals in applying Boolean Algebra to the study of circuits was to use algebraic techniques to simplify complicated systems.

Shannon believed that the more a synthesis problem can be decomposed into a combination of simple problems, the simpler the final circuits. In this paper, Shannon does just that: “By means of Boolean Algebra it is possible to find many circuits equivalent in operating characteristics to a given circuit. The hindrance of the given circuit is written down and manipulated according to the rules. Each different resulting expression represents a new circuit equivalent to the given one. In particular, expressions may be manipulated to eliminate elements which are unnecessary, resulting in simple circuits” (Shannon, 1949).

Writing further: “The most satisfactory approach to developing a block diagram is to start with a few main subdivisions of the over-all circuit and successively break these down until each block represents a unifunctional circuit…In a surprisingly large number of cases in the planning, familiar functional circuits are found to applicable. When a new circuit concept is encountered, the designer can usually recognize whether an appropriate circuit can readily be designed. If this is so, the circuit can be designated on the diagram and the design deferred until later…the attempt should be made to obtain the simplest and most efficient arrangement among the various blocks…the designer should from the start make a conscious effort to familiarize himself with different types of basic circuits already in use and to classify them in terms of function” (ibid). Item #1197

CONDITION: NY, American Telephone and Telegraph Company, 1949. Complete issue: The Bell System Technical Journal. Original printed blue wrappers. Slight fading at spine; one spot on the front wrap (see photo); otherwise fine.

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