Huge effort has been invested to come up with a wide range of design solutions that help solving the power dissipation problem for synchronous sequential circuits. Particularly, this problem is reduced to optimal coding of states of a Finite State Machine (FSM) by Boolean vectors which present sets of memory element states. Two new methods to solve the state encoding problem are proposed that minimize the average number of signal transitions on the state lines for a general State Transition Graph (STG). The method of edge cuts is an economical covering of the set of all transitions by weakly crossed edge cuts of the STG that forms set of encoding partitions on the set of the FSM states. The method of quadrates is a visual method that uses matrices of adjacency and Karnaugh maps and consists in constructing a succession of rising configurations of quadrates and edges which could serve as some fragments of the hypercube.
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