Logical design theory of NOR gate networks with no complemented inputs

It can he easily shown that any combinational circuit with only uncomplemented inputs can be realized using three stages of NOR logic. However, if such a circuit is designed by a direct extension of the theory of two-stage circuits using AND Gates and OR Gates. the result- will not be an efficient circuit. In order to design such NOR gate circuits efficiently it is necessary to modify the design techniques so that the third stage gates (those driven directly by the inputs) are. chosen properly. In partioular, it is necessary to allow for the possibility that a gate realizing. a function such as a1 + b1 be used in realizing the function ab1 + a1b as a(a1+b1) + b(a1+b1) rather than two separate gates to generate a1 and b1. A general technique for the design of such circuits is presented in this paper. Interesting features in the design of such networks arise from the fact. that their cost is effected by complementing some of the variables in the functlon.