266 research outputs found
Properties of Carry Value Transformation
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.Comment: 8 pages, 2 figures and 5 table
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