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<p>Previously proposed error detection algorithms for the residue number system require a complete recombination. A weighted approximation via the Chinese remainder theorem is shown to be sufficient to detect 100% of single errors. This makes real-time single-error diagnosis possible, which involves up to N+2 iterations of detection (N is the number of nonredundant channels). One approach uses a scaled range of L+1+log/sub 2/ (N+1) bits for detection in contrast with full decoding of approximately=L(N+1) bits, where L is the number of bits in the largest modulus. A second method forms a redundant residue number representation of the overflow multiplier A(x), although A(x) does not need to be carried through processing operations. This permits real-time single-error diagnosis and correction with a parallel array of approximately=(N+2)/sup 2/ tables.</p>
fault tolerant techniques; residue number systems; error detection algorithms; recombination; weighted approximation; Chinese remainder theorem; real-time single-error diagnosis; redundant residue number representation; parallel array; digital arithmetic; encoding; error detection; fault tolerant computing.
G.A. Orton, L.E. Peppard, S.E. Tavares, "New Fault Tolerant Techniques for Residue Number Systems", IEEE Transactions on Computers, vol. 41, no. , pp. 1453-1464, November 1992, doi:10.1109/12.177315
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