Concept Paper
Version 1
This version is not peer-reviewed
New Number System: An Extension of Binary Arithmetic
Version 1
: Received: 8 October 2024 / Approved: 9 October 2024 / Online: 9 October 2024 (14:25:57 CEST)
How to cite: Wang, H. New Number System: An Extension of Binary Arithmetic. Preprints 2024, 2024100712. https://doi.org/10.20944/preprints202410.0712.v1 Wang, H. New Number System: An Extension of Binary Arithmetic. Preprints 2024, 2024100712. https://doi.org/10.20944/preprints202410.0712.v1
Abstract
Abstract. This paper introduces $\mathbb{NS}_4$, a novel number system that extends traditional binary arithmetic by incorporating algorithmic mappings for addition, carry-over, and multiplication operations. We establish a mathematical framework demonstrating that $\mathbb{NS}_4$ forms a commutative ring, thereby extending beyond conventional number systems like complex numbers. The proposed system offers efficient representation and manipulation of numerical structures, with potential applications in computational mathematics and digital logic design.
Keywords
binary; communicative group; communicative ring
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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