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Design of Residue Generators and Multioperand Modular Adders Using Carry-Save Adders
January 1994 (vol. 43 no. 1)
pp. 68-77

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.

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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. 1, pp. 68-77, Jan. 1994, doi:10.1109/12.250610
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