Code Assignment Algorithm for Highly Parallel Multiple-Valued Combinational Circuits Based on Partition Theory (Special Issue on Multiple-Valued Logic)

Tamaki Saneaki, Kameyama Michitaka, Higuchi Tatsuo

Code Assignment Algorithm for Highly Parallel Multiple-Valued Combinational Circuits Based on Partition Theory (Special Issue on Multiple-Valued Logic)

Tamaki Saneaki

Graduate School of Engineering, Tohoku University
Kameyama Michitaka

Graduate School of Information Sciences, and Faculty of Engineering, Tohoku University
Higuchi Tatsuo

Graduate School of Information Sciences, and Faculty of Engineering, Tohoku University

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説明

Design of locally computable combinational circuits is a very important subject to implement high-speed compact arithmetic and logic circuits in VLSI systems. This paper describes a multiple-valued code assignment algorithm for the locally computable combinational circuits, when a functional specification for a unary operation is given by the mapping relationship between input and output symbols. Partition theory usually used in the design of sequential circuits is effectively employed for the fast search for the code assignment problem. Based on the partition theory, mathematical foundation is derived for the locally computable circuit design. Moreover, for permutation operations, we propose an efficient code assignment algorithm based on closed chain sets to reduce the number of combinations in search procedure. Some examples are shown to demonstrate the usefulness of the algorithm.