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arXiv · 1207.4497

Efficient Algorithms for Zeckendorf Arithmetic

Connor Ahlbach·Jeremy Usatine·Nicholas Pippenger
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Abstract

We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size and logarithmic depth. The implications of these results for multiplication, division and square-root extraction are also discussed.

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Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger. 2012-07-18. Efficient Algorithms for Zeckendorf Arithmetic. https://arxiv.org/abs/1207.4497

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