Decomposition of logic networks with emphasis on signed digit arithmetic systems

This paper describes an attempt to combine advantages of the signed digit number representation, applied at the word-level, and the residue number system applied at the digit-level, to achieve arithmetic decomposition of high-radix systems. Also introduced is a new decomposition algorithm for multiple-output Boolean functions based on partition products. Analysis of the proposed new method of arithmetic decomposition, when compared to an approach based on the theory of digit sets, reveals a more efficient use of data storage plus a higher degree of structural uniformity. The practical importance of the proposed method has been tested on a number of designs for the field programmable gate arrays. Comparison with a commercially available CAD system indicates a significant reduction in implementation complexity.