Efficient convertors for residue and quadratic-residue number systems

The quadratic-residue number system (QRNS) is known to be efficient for complex-number calculations, since it eliminates the need for cross-product terms and offers high speed with small hardware complexity. However, the conversion overhead between conventional number systems and QRNS limits its efficiency. Most implementations of convertors between QRNS and other number systems are based on ROMs or PLAs. In general, such implementations are costly and require great hardware complexity, long execution time, and high power consumption. As an alternative method, full-adder-based convertors are proposed in this paper. Full adder (FA) arrays are used to continuously decompose any power of two terms until they are represented with the same number of bits as the modulus m. FA-based convertors are shown to have less hardware complexity, execute faster, and have smaller time-complexity products than the ROM-based ones