An improved high-speed residue-to-binary converter based on the Chinese Remainder Theorem

A new high-speed residue-to-binary converter for five bit moduli based on the Chinese Remainder Theorem is presented. The orthogonal projections are computed by mapping using five-variable logic functions. The sum of projections is calculated using the Wallace tree. The output carry-save representation is partitioned into four segments in such a way that the sum of the numbers represented by the low-order segments does not exceed the Residue Number System (RNS) range M. The bits of the high-order segments are compressed by the small carry-propagate adder that in effect diminishes the size of the modulo M generator used to reduce the number represented by the high-order segments. The obtained sum is smaller than 2M, thus the effective two-operand final modulo M adder can be used. The proposed converter can be pipelined on the full-adder level.