Abstract
This article introduces the ternary logical naming convention, which was newly discovered in the study of logical units of ternary optical computers (TOCs). First, the design principle and design specification of the ternary logical naming convention are elaborated in detail and several examples are given to illustrate the use of the naming convention. Second, taking the modified signed-digit (MSD) adder of the TOC as an example, the naming convention is applied to build four ternary logical units of the MSD adder, and the implementation method of pipelined addition is introduced. Finally, the correctness of the ternary logical naming convention proposed in this paper and the usability of the adder built according to this convention are illustrated by experiments. The ternary logical naming convention can easily obtain the relationship between the ternary logic transforms, thus judging the characteristics of the logic units of TOCs, which is helpful to promote the in-depth study of TOCs in the field of numerical calculation.
Highlights
Logic is an old and dynamic field of study, which addresses judgment or reasoning and serves as the common foundation of various scientific theories [1]
Experiments show that the ternary logical naming convention proposed in this paper can be applied to the ternary optical computers (TOCs), and reconstructed logical calculators can calculate the data accurately
This paper proposes a design method for a ternary logical naming convention: combining the characteristic name of the value (CNV) and name of the transform rule (NTR) to indicate the ternary logical operation rule
Summary
Logic is an old and dynamic field of study, which addresses judgment or reasoning and serves as the common foundation of various scientific theories [1]. People have named 16 operating rules with proprietary names, such as the well-known AND, OR, NAND, and XOR. The source of these names should be closely related to the “on, off” states in the circuit, so binary logic was called “switching logic” for a long period of time. Truth tables are still widely used to express the n -valued logic operation rule. This expression method is difficult to remember, and difficult to communicate, and it is not easy to recognize the similarities and differences between different logic operations. The use of truth tables and value features to indicate logical operations is complicated and difficult to discuss
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