On the Number of Distinct State Assignments for a Sequential Machine

The determination of the number of distinct state assignments for a sequential machine has generally been made by the elimination of assignments that are the result of complementation or permutation of the state variables within a basic set of state assignments. For the D-type flip-flop, however, complementation may have an effect upon the cost of the control logic for a machine, leading, as some have interpreted it, to a new distinct state assignment. In this correspondence we reconsider the effect of complementation, showing that a new state assignment is produced only if the choice of Boolean form for the excitation expressions is restricted. This development unifies a previously unresolved question in determining the number of distinct state assignments for sequential machines that are implemented with D-type flip-flops.