EFFICIENT IMPLEMENTATION OF ARITHMETIC UNITS BASED ON POLARIZATION-ENCODED OPTICAL SHADOW-CASTING

Carry-free addition and borrow-free subtraction on the redundant modif ied signed-digit number are adopted for lensless polarization-encoded optical shadow casting (POSC). First, a new recoding truth table, whic h has a symmetrical complemented relationship between the input minter ms (entries that produce an output of 1 or -1) and their corresponding output bits, is developed for the redundant signed-digit numbers. The n, the carry-free POSC adder/subtracter is designed by determining the encoding of the redundant input bits for generating the sum/differenc e output bits and the source light-emitting-diode pattern. Two design methods are presented: direct implementation and truth-table partition ing. it is shown that the number of pixel subcells in the input encodi ng of the POSC system can be significantly reduced using the new symme trical recoding algorithm for the modified signed-digit number represe ntation. (C) 1997 Society of Photo-Optical Instrumentation Engineers.