SIGN DETECTION ALGORITHM FOR THE RNS

SIGN DETECTION ALGORITHM FOR THE RNS:

                   Sign detection plays an essential role in branching operations, magnitude comparisons, and overflow detection. Because the sign information is concealed in each residue digit in a residue number system (RNS), sign detection in an RNS is more difficult than that in the weighted number system, in which the sign is the most significant bit (MSB). Furthermore, sign detection in an RNS is not as efficient as modular operations, such as addition, subtraction, and multiplication, because of its complexity. The sign detection problem has been investigated by many researchers.

                  The modulo operations in the sign detection algorithm are bounded by size √M. In a sign detection algorithm uses the nth mixed radix digit in mixed-radix conversion (MRC) to detect the sign function. To date is the only brief to use the combinational logic to implement a sign detection algorithm based on {2^N+1 − 1, 2^N − 1, 2^N}.

             However, the method cannot be extended to other moduli sets. The moduli set {2^N+1 − 1, 2^N − 1, 2^N}, only including the types of 2ⁿ and 2ⁿ−1, has been researched extensively in recent years because of its efficiency for modulo operations and reverse conversion. In this brief, a sign detection algorithm is presented for the moduli set {2^N+1 − 1, 2^N − 1, 2^N}. First, a sign detection algorithm is presented for the restricted moduli set including modulo 2ⁿ in the RNS. The proposed sign detection algorithm requires only the addition of the modulo 2ⁿ.

   

                           

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