High-radix signed-digit arithmetic using symbolic substitution computations

Abstract

High-radix number representations such as the quaternary signed-digit (QSD) number system allow higher information storage density, less complexity, fewer system components, and fewer cascaded gates and operations. Arithmetic operations on the quaternary signed-digit are carried out using the powerful symbolic substitution scheme. A single-step or two-step conversion algorithm is employed on the QSD numbers to simplify the higher-order QSD addition process and reduce the number of the optical symbolic substitution rules. The optical addition operation of two QSD numbers is performed in one step. An efficient content-addressable memory (CAM) optical implementation of the QSD addition/subtraction operations is proposed. The QSD number addition/subtraction operations require a significantly reduced number of minterms (symbolic substitution rules) when compared to a similar previously reported technique.