Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ANALYSIS OF BINARY AND THREE-VALUED LOGIC SYSTEMS AND SOME APPLICATIONS

  • HASAN KELES (Department of Mathematics, Karadeniz Technical University)
  • Received : 2025.12.08
  • Accepted : 2026.03.13
  • Published : 2026.03.30
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Abstract

This study examines binary logic B2 = {0, 1} and three-valued logic B3 = {-1, 0, 1}, focusing on the NNOR (Neither NOR) operation for uncertainty handling. We review binary logic fundamentals and its digital circuit applications. The three-valued system B3 introduces the value -1 to encode indeterminate states. The NNOR operation propagates uncertainty through ternary arithmetic and logical circuits, enhancing computational expressiveness. Practical implementations, including half-adder/full-adder designs and circuit diagrams, demonstrate uncertainty management at the hardware level. NNOR-aware three-valued logic benefits applications requiring reasoning under incomplete information, such as fuzzy systems, AI decision-making, fault-tolerant architectures, and quantum-inspired computation. By integrating uncertainty handling into circuits, this work advances expressive and resilient computation beyond classical binary logic.

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Acknowledgement

This research received no external funding. The author would also like to thank the editor, the journal secretariat, and the anonymous reviewers for their valuable comments and suggestions.

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