Residue To Binary Conversion Using The Core Function

The core function on a residue number system is used for conversion from residue to binary or other fixed radix number systems. The decoded value is expressed as the quotient of an inner product by the core of M, where M represents the range of the system. By pre-dividing the fixed inner product coefficients by the core of M and truncating to a predetermined precision, decoding can be performed without error by table lookups followed by a summation using con- ventional binary hardware. Thus the difficulties of using the Chinese Remainder Theorem or the mixed radix conversion process are avoided, The additional computational costs of the approach are a core function evaluation and the requirement to maintain additional precision in the binary hardware.