Arithmetic binary to residue encoders for moduli (2n±2k+1)

A binary-to-residue encoder design that encodes the binary value into modulo (2ⁿ±2^k+1) residue digits is introduced. Such encoders are important for the newly introduced moduli set: (2ⁿ,2ⁿ-1,2ⁿ+1,2ⁿ-2^k+1,2ⁿ+2^k+1), where k is a positive integer, and n=2k-1. The proposed design utilises n bit carry-save adders and carry-propagate adders. A VLSI layout implementation based on 0.5 μm CMOS technology is presented. The area and delay requirements of the new encoders are shown to be less than another reported encoder.