Name
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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1155/2012/174372 | Int. J. Math. Mathematical Sciences |
Keywords | DocType | Volume |
dynamic system,equivalence relation,discrete mathematics | Journal | abs/1110.0178 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Suryakanta Pal | 1 | 0 | 0.68 |
| Sudhakar Sahoo | 2 | 51 | 13.13 |
| Birendra Kumar Nayak | 3 | 26 | 7.08 |