High-speed counters in Fibonacci numerical system

Olexiy Azarov; Olexandr Chernyak; Paweł Komada; Miergul Kozhambardiyeva; Aliya Kalizhanova

doi:10.1117/12.2280939

7 August 2017 High-speed counters in Fibonacci numerical system

Olexiy Azarov, Olexandr Chernyak, Paweł Komada, Miergul Kozhambardiyeva, Aliya Kalizhanova

Proceedings Volume 10445, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017; 1044522 (2017) https://doi.org/10.1117/12.2280939
Event: Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2017, 2017, Wilga, Poland

Abstract

Possibility of executing the carriers and borrowings by means of elementary additive transformations in the process of calculation in Fibonacci numerical system is substantiated. Methods of counting in the given numerical system, based on the usage of information redundancy are suggested. The methods consist in the fact that at every step executed all possible elementary addition transformations of code in the counter simultaneously with adding one. The suggested methods enable to construct up-, down- and up/down counters with high speed, independent on the data capacity and small hardware cost that linearly grow with the increase of the capacity. Schemes of structural organization of one digit for each of the suggested methods are given.

Citation Download Citation

Olexiy Azarov, Olexandr Chernyak, Paweł Komada, Miergul Kozhambardiyeva, and Aliya Kalizhanova "High-speed counters in Fibonacci numerical system", Proc. SPIE 10445, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017, 1044522 (7 August 2017); https://doi.org/10.1117/12.2280939

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