The general principles of the synthesis of combinatorial circuits

Abstract

By combination circuits we mean logical circuits which do not contain feedback. Existing methods for the synthesis of combination circuits cover only the first part of the problem, the construction and minimization of logical control in Boolean operations. The other steps of synthesis which are essential to electronic circuits have not been formalised. These include: 1. 1) the expression of Boolean equations in a given operator system, 2. 2) attaining the desired quality for the physical characteristics of the network, 3. 3) the comparison of different versions of the network. The existence of efficient algorithms for these steps simplifies the synthesis of actual electronic circuits satisfying given reliability criteria with the minimum use of equipment. There is also the possibility of the complete automation of the synthesis with the help of digital computers. Such a formalisation of the synthesis of electronic circuits becomes practically possible as a consequence of V.M. Glushkov's idea of giving logical operators simplified physical dependences which can be used to evaluate the quality of signals. In this paper we attempt to formalise the above steps of the synthesis. The evaluation of the quality of the signals of circuits reduces to the examination of the limits of the regions in which the values of logical variables are mapped into real physical quantities and to operations with them according to definite rules, comparable with the corresponding Boolean operations. Boolean functions are given a certain weight depending on the system of elements from which the given circuit is constructed. The different circuits corresponding to identical Boolean expressions are compared in accordance with agreed criteria. We give a general plan for the synthesis of combination circuits, and also consider some of its features applied to the elementary pulsepotential structure, as possessing the broadest set of functional elements. Let us first examine the fundamental principles of the method and then formulate an algorithm. (We use the word “circuit” below to stand for “combination electronic circuit”.)