Analog digits: bit level redundancy in a binary multiplier

The overlap resolution number system (ORNS) employs bit level residue arithmetic, and opens up a powerful approach to digital computing with analog processing elements. This new redundant representation of signals, with continuous valued digits, makes the accuracy of time sampled signal processing independent from the accuracy of the analog circuitry itself. A new proposed methodology for interfacing with binary numbers applies analog digits to digital arithmetic and introduces carry free bit level operations. Refreshment circuits warrant the validity of the analog digits, and the necessity and location of these circuits chiefly determine the complexity of a binary multiplier.