Redundant Number System‐Based Arithmetic Circuits

Abstract

Carry propagation in radix‐based number systems, like the conventional binary or decimal number systems, is the main issue that slows down the arithmetic operations. Some well‐known solutions to handle the carry propagation problem are carry look‐ahead addition, residue number systems, and redundant number systems. This chapter aims to study a variety of redundant number systems, representations, and encodings, as well as their applications and impact on the performance of digital arithmetic operations. It deals with circuit realization of redundant arithmetic operations and number encodings that facilitate design process and enhance performance. The chapter also discusses the conversion from binary to redundant number systems and the reverse. Conversion details and circuitry, greatly depends on the redundant digit set and encoding, which is used for representation of redundant digits. Furthermore, the chapter provides special arithmetic circuits such as arithmetic shifters, and gives the examples of some applications.