A new algorithm for determining all possible symmetric hybrid redundant numbers

Abstract

Number representations play important roles in improving the speed of arithmetic operations. In order to perform parallel computing, it is needed to represent the operands with fully or hybrid redundant encodings. Besides, symmetric digit set is useful in many applications. Hybrid redundant number systems can display some symmetric digit sets for radix-r. In a lemma proposed in [5] it was shown that there is no symmetric digit set [−α, α] for radix-r hybrid redundant number system with α < r − 2. However we show that the lemma can't produce all possible symmetric digit set associated with periodic hybrid redundant representations. In the paper we propose a new algorithm to determine all symmetric digit sets in hybrid redundant number system.