Feedback in Sequential Machine Realizations

Abstract

In this paper we study feedback in sequential machines that are implemented with trigger or set-reset flip-flop memory elements. A method is given for determining when a machine can be implemented with either trigger or set?reset flip-flop memory elements where the feedback in the machine is given by a Boolean function f. Several results are presented that compare the feedback when a machine is implemented with different memory elements. It is shown that if a sequential machine can be implemented with unit delay memory elements with feedback function f, then it can be realized with set-reset flip-flop with the same feedback function f. For completely specified machines, it is shown that if a machine implemented with trigger flip-flop has no feedback, then the some machine implemented with unit delays will have feedback. Conversely, if an implementation with unit delays has no feedback, then an implementation with trigger flip-flops will have feedback.