Issue No. 05 - May (1968 vol. 17)
W.A. Davis , IEEE
Abstract?This paper considers the problem of determining whether a sequential machine, given by its flow table, can be realized in the form of a single binary shift register. One-to-one and many-to-one assignments are considered. Binary partitions are introduced, and shift registers are characterized in terms of binary partitions. An algorithm is given for the determination of the required partitions for a shift-register assignment. Binary set systems are introduced and shift registers are characterized in terms of binary set systems. It is proven that there exists a sequential machine that cannot be realized by a single binary shift register of finite length. Methods for determining the set systems necessary for a single shift-register assignment are given. For machines where every state has two distinct next states, a method is presented whereby a number of machines can be easily eliminated as being not fsr realizable. It is then shown how this can be extended to all machines.
Index terms?Binary partitions, binary set systems, feedback shift registers, internal state assignment, single binary fsr's, state splitting, synchronous sequential machines.
W. Davis, "Single Shift-Register Realizations for Sequential Machines," in IEEE Transactions on Computers, vol. 17, no. , pp. 421-431, 1968.