Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SPIN HALF-ADDER IN 𝓑3

  • HASAN KELES (Department of Mathematics, Karadeniz Technical University)
  • Received : 2023.01.16
  • Accepted : 2023.05.04
  • Published : 2023.07.30
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Abstract

This study is about spin half add operations in 𝓑2 and 𝓑3. The burden of technological structures has increased due to the increase in the use of today's technological applications or the processes in the digital systems used. This has increased the importance of fast transactions and storage areas. For this, less transactions, more gain and storage space are foreseen. We have handle tit (triple digit) system instead of bit (binary digit). 729 is reached in 36 in 𝓑3 while 256 is reached with 28 in 𝓑2. The volume and number of transactions are shortened in 𝓑3. The limited storage space at the maximum level is storaged. The logic connectors and the complement of an element in 𝓑2 and the course of the connectors and the complements of the elements in 𝓑3 are examined. "Carry" calculations in calculating addition and "borrow" in calculating difference are given in 𝓑3. The logic structure 𝓑2 is seen to embedded in the logic structure 𝓑3. This situation enriches the logic structure. Some theorems and lemmas and properties in logic structure 𝓑2 are extended to logic structure 𝓑3.

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Acknowledgement

I would like to thank the editor of the Journal of Applied and Pure Mathematics and the reviewers for their contributions to the publication of the article.

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