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arXiv · 1110.0178

Properties of Carry Value Transformation

Suryakanta Pal·Sudhakar Sahoo·Birendra Kumar Nayak
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Abstract

The notion of Carry Value Transformation (CVT) is a model of Discrete Deterministic Dynamical System. In this paper, we have studied some interesting properties of CVT and proved that (1) the addition of any two non-negative integers is same as the sum of their CVT and XOR values. (2) While performing the repeated addition of CVT and XOR of two non-negative integers "a" and "b" (where a >= b), the number of iterations required to get either CVT=0 or XOR=0 is at most the length of "a" when both are expressed as binary strings. A similar process of addition of Modified Carry Value Transformation (MCVT) and XOR requires a maximum of two iterations for MCVT to be zero. (3) An equivalence relation is defined in the set (Z x Z) which divides the CV table into disjoint equivalence classes.

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Suryakanta Pal, Sudhakar Sahoo, Birendra Kumar Nayak. 2011-10-02. Properties of Carry Value Transformation. https://arxiv.org/abs/1110.0178

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