A map approach to the solution of a class of boolean functional equations

Typically, simultaneous Boolean equations are expressed by a set of relations Fi = fi, i = 1,2 ¿, where the Fi and fi are switching functions of N binary variables. In many logical design problems, a special type of Boolean equation is often encountered; namely, F(A0, A1 ¿, An¿1, X0, X1 ¿, Xm¿1) = f(a1, a2 ¿, ak, X0, X1 ¿, Xm¿1), in which the arguments Ai´s and Xi´s are binary variables and the a1´s are implicit functions of the Ai´s only. This paper presents a somewhat new approach to solving such special types of Boolean functional equations. The solution function (see reference 1) can be formulated and mapped on a Veitch chart, especially tailored to the present problem, and all possible sets of solutions of the implicit functions ai´s which satisfy the original functional equation are obtained simultaneously. Other possible applications and extensions of this method are discussed also.