On the Reduction of Arithmetic Operations to Signed Addition
Abstract
This paper demonstrates that all four fundamental arithmetic operations—addition, subtraction, multiplication, and division—can be reduced to a single primitive: addition with explicit sign interpretation. By disentangling operator semantics from sign semantics, it becomes evident that subtraction, multiplication, and division are not autonomous processes but derived forms of iterative or negated addition. Through this unifying perspective, the traditional sign rules—often taught as isolated conventions—emerge as direct consequences of structural logic. Furthermore, the same reduction mirrors the architecture of digital arithmetic logic units (ALUs), which rely on addition as the atomic hardware operation. The resulting framework offers conceptual simplicity, didactic clarity, and architectural coherence.
Citation
Stepan, R. (2025). On the Reduction of Arithmetic Operations to Signed Addition.
Zenodo. https://doi.org/10.5281/zenodo.17612069
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Version Notes
- Version: 1.0
- Last updated: 2025
Katalogeintrag & Dokumentfassungen
Konzeptionelle Untersuchung der Darstellung elementarer arithmetischer Operationen durch Addition mit expliziter Vorzeichensemantik. Die unterschiedlichen Manuskriptfassungen bleiben nachvollziehbar zugeordnet.