In this paper a new theory referred to as the decrease-radix design (DRD) is proposed, which is found in the research of logic units of ternary (tri-valued) optical computer. Based on the theory proposed, the principles and the regulations of the DRD for making operation units of multi-valued operation with carrying/borrowing free are also presented. The research work has come to the following important conclusion: let D be a special state contained in n physical informative states, then one may figure out any multi-valued processors within n (n×n) carrying/borrowing free n-valued units by the composition some of n×n×(n−1) simplest basic operating units according to the regulations of DRD proposed in this paper. The detailed systematic way of our design regulations is highlighted step by step in the paper with an example of design of a tri-valued logic optical operating unit. The real architecture, the procedure, and the experimental results of our sample in tri-valued logic operating unit are given. Finally, a re-constructible model of ternary logical optical processor is introduced. The theory proposed in the paper has laid down a solid foundation for the design of re-constructible carrying/borrowing free operating units in ternary optical computers and can be widely used as the designing reference in a variety of multi-valued logic operating units.carrying/borrowing free operating units, decrease-radix design, re-constructible, ternary optical computer

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