Abstract
The symbol substitution (SS) rules necessary for the addition and subtraction of higher-order modified signed-digit (MSD) numbers are derived. The derived higher-order SS rules are made carry-free by taking into consideration a pair of reference bits from the next-lower-order bit position. The proposed technique employs a two-step operation that is independent of the length of the bit string to be processed, and thus is very fast. In the first step, the higher-order SS rules are used to map the number strings to be added (subtracted) into an intermediate pair, and these numbers are added bit-wise to yield the final result. A CAM-based optical implementation scheme may be used for the processing. For real-time processing, a joint-transform-correlator-based optical system may also be used. The proposed scheme can be easily extended to other higher-radix MSD number systems. (P.D.)