Design of high-speed digital circuits such as adders and multipliers is one of the most important issues to implement high performance VLSI systems. This paper proposes a new multiple-valued code assignment algorithm to implement locally computable combinational circuits for k-ary operations. By the decomposition of a given k-ary operation into unary operations, a code assignment algorithm for k-ary operations is developed. Partition theory usually used in the design of sequential circuits is effectively employed for optimal code assignment. Some examples are shown to demonstrate the usefulness of the proposed algorithm.

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.