Arithmetic with signed analog digits

This paper presents mathematical foundations of the Overlap Resolution Number System (ORNS) which is based on signed continuous valued digits (CVDs). ORNS is a redundant number system employing residue arithmetic. In contrast to the implementation of arithmetic by binary or multiple-valued logic circuits, arithmetic operations in this novel number system are performed by analog digit manipulation circuitry. The redundancy in an ensemble of continuous valued digits that comprises a number provides tolerance to implementation imprecisions. Processing with these analog digits is performed by carry-free arithmetic structures with systematic circuit level redundancy.