Parallel optical computing using recoded trinary signed-digit numbers

We propose a simple recoded trinary signed-digit number representation for parallel optical computing. This technique performs multidigit carry-free addition and borrow-free subtraction in constant time, using only 50% of the, minterms required in the most recently reported trinary signed-digit arithmetic technique. One may use a single-step optoelectronic or a two step all-optical architecture to implement the proposed technique.