Investigation into efficient conversion methods between residue and binary systems
Gilbert, David E.
Butler, Jon T.
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Residue number systems (RNS) can efficiently perform addition, subtraction, and multiplication in a parallel and fault tolerant manner. Because of this, they hold significant promise for use in digital signal processing, where high speed arithmetic operators are needed. However, the difficulties in using RNS, such as magnitude comparison between two RNS values, division, and determining overflow or underflow out of system range, have prevented more widespread use of these systems. This thesis investigates traditional methods to perform comparisons and to propose some new ones. Proposals include residue number system with quotient (RNS-Q), residue number system quotient-on-demand (RNS-QD), and pipelined conversions from traditional RNS to a mixed radix representation. These proposals will be compared with traditional methods with respect to silicon area needed for implementation, speed with which they can be developed, and VLSI techniques utilized to carry out the design.
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