A Family of High Radix Signed Digit Adders

Signed digit (SD) number systems allow for high performance carry-free adders. Maximally redundant SD (MRSD) alternatives provide maximal encoding efficiency among Radix-2^h SD number systems, whereby value of h tunes the area-time trade-off. Straightforward implementation of the conventional carry-free addition algorithm requires three O(log h) addition-like operations in sequence. However, there are several MRSD implementations with only one such operation. Some of them are delay optimized, but suffer from extensive hardware redundancy, while some other equally fast adders show less power/area consumption. A careful study of the latter cases hints on variety of improvement options, based on which and a new transfer computation technique, we develop a family of faster MRSD adders that consume less power/area than all the previous relevant works. They also fit efficiently within the redundant digit floating point addition scheme. However, similar to their relevant ancestor designs, suffer from an inherent property of MRSD adders, i.e., difficulty of handling hidden leading zero-digits. To remedy this problem, we use less redundant SD representations, where our transfer extraction method applies efficiently and leads to far less complex leading zero-digit detection. All the presented designs are supported by exhaustive correctness tests and performance evaluation via 0.13 micrometer CMOS technology synthesis.