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A signed-digit architecture for residue to binary transformation

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1 Author(s)
Pourbigharaz, F. ; Semicond. Corp., Ont., Canada

A residue to binary converter architecture based on the Chinese Remainder Theorem (CRT) is presented. This is achieved by introducing a general moduli set Sk Sk={2m-1, 22om+1, 221m+1, 222m+1,....,222km +1} for Residue Number System (RNS) applications. Residue to binary converter architectures based on moduli sets So={2m-1, 2m+1} and S1=(2 m-1, 2m+1, 22m+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

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Computers, IEEE Transactions on  (Volume:46 ,  Issue: 10 )