A Construction Theory of Multiple-Valued Logic Sequential Machines on $GF(2^M)$

This pper presents a method for constructing multiple-valued logic sequential machines based on Galois field. First, we assign all elements in GF(2**m) to bit codes using mathematical properties of GF(2**m). Then, we realized the sequencial machine circuits with and withoutm feed-back. 1) Sequential machines with feed-back are constructed by using only MUX from state-transition diagram expressing the information of sequential machines. 2) Sequential machines without feed-back are constructed by following steps. First, we assigned states in state-transition disgram to state bit codes, then obtained state function and predecessor table explaining the relationship between present states and previous states. Next, we obtained next-state function from state function and predecessor table. Finally we realized the circuit using MUX and decoder.