On the optimality of ternary arithmetic for compactness and hardware design

In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as the main parameter to assess the efficiency of the representa...

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Bibliographic Details
Published inarXiv.org
Main Author Georgiou, Harris V
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.10.2016
Subjects
Arithmetic
Formulations
Hardware
Logarithms
Optimization
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Summary:In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as the main parameter to assess the efficiency of the representation, in terms of information compactness and estimated implementation cost in hardware. Using proper formulations for the optimization task, the universal constant 'e' (base of natural logarithms) is proven as the most efficient radix and ternary is asserted as the closest integer choice.
ISSN:2331-8422