VLSI Digital Signal Processing Systems: Design and Implementation

14.1    INTRODUCTION

In a conventional nonredundant radix-r number system, a digit can take on values {0,1,···,r – 1}, and all the numbers can be represented in a unique way. A radix-r redundant signed-digit number system is based on a digit set , where the notation denotes –x, 1 ≤ β,α ≤ r – 1, and the digit set S contains more than r values [1]. The last condition allows multiple representations for any number in signed-digit format, thus the name redundant. A symmetric signed-digit representation (α = β) is generally used and considered in this chapter. For example, the digit set {,0,1} is used for radix-2 (r = 2) redundant number system. In this case, the number 3 can be represented as 0011 or 010, etc. Signed-digit representations have been used in Chapter 13 in the context of CSD representation and Booth recoding; however, these representations are unique.

The attractiveness of the redundant signed-digit number systems lies in their “carry-free” addition property. This feature makes them very useful in digit-serial implementation of division and square root operations where the computations ...