## Abstract

Residue Number System (RNS) based implementation of DSP algorithms have been presented in the literature [29, 30, 92] as a technique for high speed realization. In a Residue Number System (RNS), an integer is represented as a set of residues with respect to a set of integers called the Moduli. Let (
we use notation
where M is the dynamic range of the given moduli set. So, the moduli set is determined based on the bit-precision needed for the computation. For example, for 19-bit precision the moduli set 5,7,9,11,13,16 can be used [87].

*m*_{1},*m*_{2},*m*_{3}, ...,*m*_{n}) be a set of relatively prime integers called the Moduli set. An integer X can be represented as*X =*(*X*_{1},*X*_{2},*X*_{3}, ... ,*X*_{n}) where$$ {X_i} = \left( X \right)\;modulo\;{m_i}\;for\;i = 1,2, \ldots ,n $$

(7.1)

*X*_{i}to represent |*X*|_{mi}the residue of*X*w.r.t m_{i}. Given the moduli set, the dynamic range(M) is given by the LCM of all the moduli. If the elements are pair-wise relatively prime, the dynamic range is equal to the product of all the moduli [92]. The bit-precision of a given moduli set is$$ bits = lo{g_2}\left( M \right) $$

(7.2)

## Keywords

Residue Number System Coefficient Optimization Area Improvement Redundancy Elimination Reduce Power Dissipation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 2001