Zero, Sign, And Overflow Detection Schemes For Generalized Signed-digit Arithmetic
Behrooz Parhami · 2005
A generalized signed-digit (GSD) number system uses the digit set {-a,-a+l, ... , el, p} in radix-r positional notation, with a$> 0 and p=a+P+l-r > 0. Most GSD number systems support carry-free addition and borrow-free subaaction and even those that do not, can be dealt with using limited-propagation algorithms which yield the ith sum or difference digit as a function of three consecutive digits in each of the operands. Thus, GSD number systems are suitable for realizing high-speed special-purpose arithmetic engines in VLSI. To do this, the arithmetic operations of addition and subtraction must be supported by zero, sign, and overflow detection procedures. Algorithms for the implementation of these support functions are presented in this paper.