Optoelectronics recoded trinary signed-digit adder using optical correlators

A symbolic substitution based optoelectronics numeric processor using the recoded trinary signed-digit (TSD) number representation is presented. The proposed technique performs parallel carry-free addition in constant time, independent of the operand length. The proposed trinary adder is more efficient compared to a similar alternate technique that uses the modified signed-digit (MSD) number representation. The trinary adder is compact since it employs only one correlator rather than three correlators as it was reported for the MSD counterpart. Further, it can handle much larger dynamic range since TSD uses much fewer digits than MSD in its representation for the same decimal numbers