Cascade realizations of two-valued input multiple-valued output functions using decomposition of group functions

This paper considers a method to realize a two-valued input three-valued output function f:{0, 1}ⁿ→{0, 1, 2} by using a cascade of four-input cells. Decomposition of a group function is used to find a canonical form. We show that the Walsh spectrum specifies the canonical form, and the number of non-zero coefficients in the spectrum is proportional to the number of cells in the cascade. Finally, we show a design algorithm for a p-valued function f:{0, 1}ⁿ→{0, 1, ..., p-1}. The designed cascades are reversible and conservative.