A Proposal for Ternary ("1-2-3") Computation as a Coherent Alternative to Binary Logic

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Authors: Joel Lesperance
Cited by: 0

Abstract

Modern digital computing is built almost entirely on binary logic, using the two-symbol set {0,1}. Binary became dominant for historical and engineering reasons: it is easy to implement electronically, it tolerates noise well, and it aligns cleanly with Boolean algebra. However, mathematical optimality is a different question from engineering convenience. This paper proposes and explores a simple, logically clean ternary computational framework based on the ordered set {1,2,3}, rather than {0,1}. We examine how ternary logic encodes information, how arithmetic behaves in this representation, how zero emerges as a relational outcome rather than a primitive value, and why this system aligns naturally with divisibility structures that underlie many real-world cyclic and modular processes — including systems expressible in base-12. Our thesis is intentionally modest and testable: ternary computation has the potential to reduce representational redundancy, shorten instruction chains, and improve energy efficiency in classes of problems involving modularity, cyclic symmetry, and dense encoding structures. We propose practical lines of research for evaluating ternary architectures side-by-side with binary hardware and software, and invite empirical assessment rather than philosophical debate.

Fields of Study & Subjects

Computability Logic AI Algorithms DNA and Biological Computing Cellular Automata and Applications

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
4 January 2026