Principle of a one-step MSD adder for a ternary optical computer

While investigating a three-step MSD adder and the reliability thereof for ternary optical computers（TOC）, the principle of one-step MSD addition was found. An important concept, the mid-bit transform, is proposed. Next, the important mid-bit transform table（MTT） for 3-bit MSD input and the corresponding mid-bit transform unit（MTU） are obtained. Using the principle, the concept structure of a one-step MSD adder is proposed such that the sum of the addition can be obtained easily in one step in parallel. By restricting the input symbols, a simplified MTT is obtained and the principle of a one-step adder with restricted input symbols is introduced, together with the corresponding simplified concept structure of a one-step MSD adder. Two examples are presented to demonstrate the principles of one-step MSD adders. This work lays the theoretic foundation for the design of an optical MSD adder in future study.