Sequential circuit realizations with pulse input fundamental mode sequential circuits

Summary This paper gives a unified treatment for electronic sequential circuit realizations and suitable procedures for synthesizing them. This is done by showing that every sequential circuit operating in synchronous mode can be transformed into an equivalent sequential circuit operating in fundamental mode with the same number of internal states. The basic idea is to consider, for both the major types of sequential circuits, circuits having pulse inputs—PS circuits for sequential circuits operating in synchronous mode, andPF circuits for sequential circuits operating in fundamental mode—and to investigate the relationship between them. A concurrent and a self concurrent operation is defined forPF circuits, and it is shown that any synchronon mode sequential circuit can be transformed into an equivalent normal or self-concurrentPF circuit realization inherently free ofessential hazards and critical races. Moreover, it is seen that static hazards that can influence the circuit operation can be detected and eliminated by formal methods. The circuit realizations discussed in this paper are composed by a defined number of subcircuits, and it is shown that these subcircuits can in turn be decomposed to obtain circuit realizations with flip-flops or register elements. Finally, it is shown that by similar methods level-input fundamental mode sequential circuits can also be transformed into self-concurrentPF circuit realizations in order to eliminate essential hazards and critical races. This paper has been communicated at the ?Colloque d'Algebre de Boole?, Grenoble, January 11–15, 1965, and reported in the C.S.C.E. Internal Report II. 9. May, 1965.