Polarization-encoded optical shadow-casting: an efficient implementation of carry-free arithmetic

The carry-free addition and borrow-free subtraction on the redundant binary number is adopted for the lensless polarization-encoded optical shadow-casting (POSC). First, a new recoding truth-table which has a symmetrical complemented relationship between the input minterms (entries that produce an output of 1 or -1) and their corresponding output bits is developed for the redundant signed-digit numbers. Then, the carry-free POSC adder/subtracter is designed by determining the encodings of the redundant bits for generating the sum/difference output bit and the source LEDs pattern. Two design methods are presented: direct implementation and truth-table partitioning. It is shown that the design of the POSC carry-free adder/subtracter has much less pixel subcell (six) in the coding pattern of the POSC system than the previously designed carry-free adder (twelve)