On a Method of Decomposition of Boolean Functions into Unate Functions for Synthesis with Threshold Logic Elements†
DEBABRATA SARMA, SUNIL RANJAN DAS, Avik Kumar Choudhury · International Journal of Control · 1966
The present paper is basically concerned with the problem of decomposition of general Boolean functions into unate sub-functions and a study of the associated properties. It is shown that the primary information regarding such a decomposition into unate functions can be had from the cover table representation of the given function. It is also shown how a knowledge of some of the geometrical properties of Boolean functions greatly facilitates recognition of threshold functions in certain special cases. A simplified procedure is finally suggested for realizing a given Boolean function with a fewer number of threshold logic elements. At every stage examples are worked out to show the decomposition and the recognition procedures and to illustrate the synthesis method.