Abstract

Carry-free arithmetic operations using modified signed-digit (MSD) number representation are performed. The MSD arithmetic-based flagged symbolic substitution,¹ where an additional bit is used along with each pair of the input bits to characterize the next less significant pair of bits, is implemented using the polarization-encoded optical shadow-casting system (POSC).² Two different designs using the POSC scheme are proposed for implementing the MSD addition and subtraction. The input codes and source patterns for the POSC system are determined for both an MSD adder and MSD subtracter. The design process consists of grouping the rows of the MSD adder/subtracter truth table in terms of an overlap operation² so that the solution of the corresponding overlap equation yields the input pixel encoding of the POSC system for a particular output mask and a fixed source pattern for achieving the desired arithmetic output.

© 1988 Optical Society of America