Abstract

Among the higher radix number systems, the trinary modified signed-digit (MSD) arithmetic appears to be the most promising in terms of both optical processing elements and storage complexity.¹ The MSD system involves two processing steps which can be optically implemented using the recognition and substitution phases of symbolic substitution. Recently, Kozaitis² and Eichmann et al.³ demonstrated higher-order SS based addition schemes that allow longer operands to be processed at the same time. However, the processing time for these SS schemes is still a function of the operand length. To overcome these problems, we propose a conditional higher-order trinary MSD SS scheme. In this technique, the two-step arithmetic operations (addition and subtraction) achieved are independent of the operand length. The necessary SS rules for addition (subtraction) is made carry-free (borrow-free) by checking a pair of reference bits from the next lower order bit so that there are no two identical nonzero MSD digits in any column. This scheme is efficient in terms of memory requirement since more information can be incorporated in fewer digits. Finally, a content addressable memory based optical implementation of the trinary MSD SS scheme is also presented.

© 1991 Optical Society of America