High-speed counters in Fibonacci numerical system

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

2017

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DOI 10.1117/12.2280939
Data confidence 70 medium
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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.