Issue No. 01 - January (1994 vol. 43)

ISSN: 0018-9340

pp: 68-77

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.250610

ABSTRACT

<p>Residue generator is an essential building block of encoding/decoding circuitry for arithmetic error detecting codes and binary-to-residue number system (RNS) converter. In either case, a residue generator is an overhead for a system and as such it should be built with minimum amount of hardware and should not compromise the speed of a system. Multioperand modular adder (MOMA) is a computational element used to implement various operations in digital signal processing systems using RNS. A comprehensive study of new residue generators and MOMA's is presented. The design methods given here take advantage of the periodicity of the series of powers of 2 taken module A (A is a module). Four design schemes of the n-input residue generators mod A, which are best suited for various pairs of n and A, are proposed. Their pipelined versions can be clocked with the cycle determined by the delay of a full-adder and a latch. A family of design methods for parallel and word-serial, using similar concepts, is also given. Both classes of circuits employ new highly-parallel schemes using carry-save adders with end-around carry and a minimal amount of ROM and are well-suited for VLSI implementation. They are faster and use less hardware than similar circuits known to date. One of the MOMA's can be used to build a high-speed residue-to-binary converter based on the Chinese remainder theorem.</p>

INDEX TERMS

adders; digital arithmetic; residue generators; multioperand modular adders; carry-save adders; arithmetic error detecting codes; binary-to-residue number system; residue generator; Chinese remainder theorem; arithmetic codes; residue number system; residue arithmetic.

CITATION

S.J. Piestrak, "Design of Residue Generators and Multioperand Modular Adders Using Carry-Save Adders",

*IEEE Transactions on Computers*, vol. 43, no. , pp. 68-77, January 1994, doi:10.1109/12.250610