Optical adders using a modified signed-digit(MSD) number system have been proposed to restrict the carry propagation chain encountered in a conventional binary adder to two positions to the left. But, MSD number system must encode three different states to represent the three possible digits of MSD. In this paper, we propose the design of an optical adder based on 1-bit addition rules by using the method of symbolic substitution (SS). We show that this adder can use binary input which is used by a digital computer, as it is and be implemented by smaller system in size than MSD adder.