New fault tolerant techniques for residue number systems

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+log₂ (N+1) bits for detection in contrast with full decoding of ≈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 ≈(N+2)² tables