Optimal table lookup schemes for VLSI implementation of input/output conversions and other residue number operations

Residue number representation has become a viable alternative for fast, area-efficient VLSI realization of high-performance signal processing hardware. Wider applicability and improved cost/performance of residue-based VLSI implementations of signal processing algorithms are critically dependent on efficient realization of I/O data conversions and several other support functions that are treated in this paper. Alternate table-lookup schemes for conversion of binary to residue numbers, and vice versa, are presented. Input widths of lookup tables can be changed freely through a repartitioning scheme to provide tradeoffs between table size (area) and computation speed. Improved variants of VLSI-based pipelined binary-to-residue converters are derived along with balanced, highly regular, pipelined architectures for residue-to-binary conversion in VLSI. The input repartitioning method is shown to be applicable to other important residue number system operations, including sign detection, mixed-radix conversion, and base extension.