This paper proposes a generic algorithm for converting the redundant number representation into the complement number representation using "on-the-fly" architecture, which can be taken place in parallel. This method can solve the carry propagation problem occurring in the conventional conversions, which are sequential algorithms. The detail in this paper shows that the conversion is computable by the "on-the-fly" technique and lead to a faster computation time. Moreover, the proposed methodology can perform the conversion of a number in any integer radix into the complement representation. The mathematical proofs of the proposed algorithm in terms of correctness are also included in this paper.
Redundant number system was proposed in order to solve the carry-propagation problem. Although it provides a carry-free parallel addition, this representation requires a lot of space to store itself. Many conversions from the redundant number system into another number representation have been introduced to decrease the storage usage. This paper proposes a generic algorithm in order to convert the redundant number representation into the complement number representation. The proposed algorithm can perform the conversion of a number in any integer radix and eliminates the carry chain of the traditional method. The proofs of the proposed algorithm in term of correctness are also included in this paper.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.