RSNS-to-Binary Conversion

The robust symmetrical number system (RSNS) is a symmetrical number system formed such that only one element in each RSNS vector changes between code transitions. This integer Gray-code property makes the RSNS useful in analog-to-digital converters (ADC), direction finding antenna architectures and electro-optical ADCs since it eliminates any encoding errors that can occur when the input signal lies about any code transition point. One of the fundamental difficulties in a hardware application of the RSNS, such as an ADC, is the conversion of the RSNS residue vectors into a more convenient representation such as a binary number. By exploiting the one-to-one correspondence between the RSNS and the residue number system, an efficient process for conversion of the symmetrical residues is formed. The conversion process presented in this paper produces a hardware implementation that is at least an order of magnitude smaller in terms of transistor count than read-only-memory conversion methods, and is easily pipelined to achieve fast conversion speeds.