A signed-digit architecture for residue to binary transformation

A residue to binary converter architecture based on the Chinese Remainder Theorem (CRT) is presented. This is achieved by introducing a general moduli set S^k S^k={2^m-1, 2^2om+1, 2^21m+1, 2^22m+1,....,2^22km +1} for Residue Number System (RNS) applications. Residue to binary converter architectures based on moduli sets S^o={2^m-1, 2^m+1} and S¹=(2 ^m-1, 2^m+1, 2^2m+1) are developed. The conversion procedure is performed in the following three levels: residue to signed-digit, signed-digit to binary, end-around carry addition/subtraction. In the first level of operation, the signed-digit representation of the CRT equation is realized by using redundant adder/subtracter blocks. Here, the necessary embedded multiplications are replaced by simple shift-left operations and the carry propagation is totally eliminated. In the second level, the redundant representation of CRT is directly converted to binary format. Finally, an end-around carry (EAC) addition/subtraction is performed to obtain the result at the third level of operation. The proposed architectures are simple, fast, free of memory blocks and module adders