Logic circuits in the plane

Abstract

There are, essentially, just 17 subsets of the 16 binary logical operations which are both (a) complete in the sense that any n-variable logical function can be expressed with them and (b) minimal, subject to (a). For each of these bases, it is shown how to construct, for any logical function F, a planar logical circuit with gates from that base alone which realizes F. This is done by constructing a planar crossover circuit for each minimal base. Minimality of the crossover circuits is discussed.