The limitations in electronics in arithmetic, algebraic & logic processing are well known. Very high speed performance (above GHz) are not expected at all in conventional electronic mechanism. To achieve high speed performance we may think on the introduction of optics instead of electronics for information processing and computing. Non-linear optical material is a successful candidate in this regard to play a major role in the optically controlled switching systems and therefore in all-optical parallel computation these materials can show a very good potential aspect. In this paper, we have proposed a new method of an optical half adder as well as full adder circuit for binary addition using non-linear and linear optical materials.