A State Assignment Technique for Sequential Machines Using J-K Flip-Flops

Several techniques for choosing state assignments which tend to minimize the combinational input and output circuitry of sequential machines have been developed. One of these techniques is a heuristic scoring approach which was originally developed assuming delays as memory elements [1]. This technique was later expanded to cover the cases when trigger flip-flops or combinations of trigger flip-flops and delays were used as memory elements [2]. In this correspondence the hueristic scoring approach developed by Dolotta and McCluskey will be expanded to cover the case when J-K flip-flops are used as memory elements. It will be shown that the relative importance of various features when using delays as memory elements is not the same as when J-K flip-flops are used. Also, a new set of scores for J-K flip-flops based on the relative importance of various features will be developed. When delays are used as memory elements, the following octal scores are assigned for various features: 20 for an all-zero entry 10 for an all-one entry 20 for adjacency 4 for identity with the base entry 4 for complement of base entry. Each feature will now be examined to see how it applies when J-K flip-flops are used, and new scores will be assigned to some features. With J-K flip-flops, if a column entry is identical to a base entry, the JandK inputs of the flip-flop will be ZERO's and DON'T CARE's. This is equivalent to the condition which exists for an all-zero entry when delays are used as memory elements. Thus when J-K flip-flops are used, identity with the base entry will be given a score of octal 20. For an all-zero column entry, when J-K flip-flops are used, the J inputs will be ZERO's and DON'T CARE's and the K inputs will be ONE's and DON'T CARE's. Similarly, for an all-one column entry, the J inputs will be ONE's and DON'T CARE's and the K inputs will be ZERO's and DON'T CARE's. Since the occurrence of a one onaJorKinputmay require a gate function, an all-zero or all-one column entry is not as desirable as a column entry which is identical to the base entry. If a column entry is the complement of a base entry when using J-K flip-flops, both the J and K inputs will be ONE's and DON'T CARE's.