The Synthesis of Two Terminal Switching Circuits

HE theory of switching circuits may be divided into two major divisions, analysis and synthesis. The problem of analysis, determining the manner of operation of a given switching circuit, is comparatively simple. The inverse problem of finding a circuit satisfying certain given operating conditions, and in particular the best circuit is, in general, more difficult and more important from the practical standpoint. A basic part of the general synthesis problem is the design of a two-terminal network with given operating characteristics, and we shall consider some aspects of this problem. Switching circuits can be studied by means of Boolean Algebra. 1 - 2 This is a branch of mathematics that was first investigated by George Boole in connection with the study of logic, and has since been applied in various other fields, such as an axiomatic formulation of Biology, 3 the study of neural networks in the nervous system, 4 the analysis of insurance policies,5 probability and set theory, etc. Perhaps the simplest interpretation of Boolean Algebra and the one closest to the application to switching circuits is in terms of propositions. A letter X, say, in the algebra corresponds to a logical proposition. The sum of two letters X + F represents the proposition "X or F" and the product XY represents the proposition "X and F " . The symbol X' is used to represent the negation of proposition X, i.e. the proposition "not X". The constants 1 and 0 represent truth and falsity respectively. Thus X + F = 1 means X or F is true, while X + YZ' = 0 means X or (F and the contradiction of Z) is false.