A Parallel Residue-to-binary Converter for the Moduli Set {(2^m) - 1, 2^((2^0)m)+ 1, 2^((2^1)m) + 1, . . ., 2^((2^k)m)+ 1}

In this paper, a high-speed parallel residue-to-binary converter is proposed for a recently introduced moduli set S^k = {2^m – 1, 2^(20m)+ 1, 2^(21m) + 1, . . ., 2^(2km)+ 1} for a general value of k. The proposed converter uses simple cyclic shift and concatenation operations and does not require any multiplier. Individual converters for the cases of k = 0 and k = 1 are derived from the general architecture and compared with those existing in the literature. The converter for S^0 is twice as fast requiring only one-half of the hardware, while that of S^1 is three times as fast, but requiring only 60% of the hardware, as compared to the corresponding ones existing in the literature. Furthermore, the proposed converters are implemented using 0.5-micron CMOS VLSI technology. Based on S^0, the layouts for 8-bit, 16-bit, 32- bit and 64-bit converters are generated, and the corresponding simulation results obtained.

關鍵字

VLSI implementation ； Computer arithmetic ； Parallel algorithm ； Residue number system ； Chinese remainder theorem ； Digital signal processing

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A Parallel Residue-to-binary Converter for the Moduli Set {(2^m) - 1, 2^((2^0)m)+ 1, 2^((2^1)m) + 1, . . ., 2^((2^k)m)+ 1}

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