Geodesic
Fibonacci Counter Based on Zeckendorf's Theorem (Boolean Realization)
The purpose of this article is to present the research results on the development of the original noise-immune Fibonacci counter based on Zeckendorf's Theorem. The main peculiarity of the counter consists in the fact that we use only the socalled minimal forms of the Fibonacci code for error detection what increases noise immunity and informational reliability. The Fibonacci counter demonstrates significant benefits in comparison with the known Fibonacci counters based on the “convolutions” and “devolutions,” both in speed and error detection ability. The Fibonacci counter can be the important step for designing noise-immune Fibonacci microcontrollers and microprocessors.
Classification : 68M15, 68M20, 68P30, 11T71, 94B60
Keywords: Fibonacci numbers, Zeckendorf's Theorem, Fibonacci code, Fibonacci counter, Fibonacci computers 
@article{VM_2014_16_2_a0,
     author = {Alexey Stakhov and Alexey Borisenko and Svetlana Matsenko},
     title = {Fibonacci {Counter} {Based} on {Zeckendorf's} {Theorem} {(Boolean} {Realization)}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2014_16_2_a0/}
}
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Alexey Stakhov; Alexey Borisenko; Svetlana Matsenko. Fibonacci Counter Based on Zeckendorf's Theorem (Boolean Realization). Visual Mathematics, Tome 16 (2014) no. 2. http://geodesic.mathdoc.fr/item/VM_2014_16_2_a0/