Optimum State Assignment for the D Flip-Flop

This correspondence is a modification of the basic SHR-optimal¹ state assignment procedure for the D flip-flop. Under the minimum sum-of-products (MSOP) constraint, a sequential machine with n D flip-flops has 2ⁿ times as many distinct state assignments and twice as many distinct state assignment columns as the other flip-flop types. This correspondence shows that even though the D flip-flop machine has 2ⁿN total distinct state assignments, the costs of these assignments can be uniquely determined by examination of only N of these assignments. Integration of this concept into the basic SHR-optimal algorithm produces a computational saving on the order of 2^n-1 times.