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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.
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 of 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.