Computer Science – Discrete Mathematics
Scientific paper
2011-10-02
Computer Science
Discrete Mathematics
8 pages, 2 figures and 5 tables
Scientific paper
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.
Nayak Birendra Kumar
Pal Suryakanta
Sahoo Sudhakar
No associations
LandOfFree
Properties of Carry Value Transformation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Properties of Carry Value Transformation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Properties of Carry Value Transformation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-284179