Properties of Carry Value Transformation
Carry Value Transformation (CVT) is a model of discrete deterministic dynamical system. In the present study, it has been proved that (1) the sum of any two nonnegative integers is the same as the sum of their CVT and XOR values. (2) the number of iterations leading to either CVT=0 or XOR=0 does not...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/174372 |
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| author | Suryakanta Pal Sudhakar Sahoo Birendra Kumar Nayak |
| author_facet | Suryakanta Pal Sudhakar Sahoo Birendra Kumar Nayak |
| author_sort | Suryakanta Pal |
| collection | DOAJ |
| description | Carry Value Transformation (CVT) is a model of discrete deterministic dynamical system. In the present study, it has been proved that (1) the sum of any two nonnegative integers is the same as the sum of their CVT and XOR values. (2) the number of iterations leading to either CVT=0 or XOR=0 does not exceed the maximum of the lengths of the two addenda 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 shown to exist on Z×Z which divides the CV table into disjoint equivalence classes. |
| format | Article |
| id | doaj-art-79a124e7393d4ea1874873cb858dc15c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-79a124e7393d4ea1874873cb858dc15c2025-08-20T02:07:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/174372174372Properties of Carry Value TransformationSuryakanta Pal0Sudhakar Sahoo1Birendra Kumar Nayak2Department of Basic Science and Humanities, Silicon Institute of Technology, Silicon Hills, Patia, Bhubaneswar 751024, IndiaDepartment of Computer Science, Institute of Mathematics and Applications, Andharua, Bhubaneswar 751003, IndiaP.G. Department of Mathematics, Utkal University, Bhubaneswar 751004, IndiaCarry Value Transformation (CVT) is a model of discrete deterministic dynamical system. In the present study, it has been proved that (1) the sum of any two nonnegative integers is the same as the sum of their CVT and XOR values. (2) the number of iterations leading to either CVT=0 or XOR=0 does not exceed the maximum of the lengths of the two addenda 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 shown to exist on Z×Z which divides the CV table into disjoint equivalence classes.http://dx.doi.org/10.1155/2012/174372 |
| spellingShingle | Suryakanta Pal Sudhakar Sahoo Birendra Kumar Nayak Properties of Carry Value Transformation International Journal of Mathematics and Mathematical Sciences |
| title | Properties of Carry Value Transformation |
| title_full | Properties of Carry Value Transformation |
| title_fullStr | Properties of Carry Value Transformation |
| title_full_unstemmed | Properties of Carry Value Transformation |
| title_short | Properties of Carry Value Transformation |
| title_sort | properties of carry value transformation |
| url | http://dx.doi.org/10.1155/2012/174372 |
| work_keys_str_mv | AT suryakantapal propertiesofcarryvaluetransformation AT sudhakarsahoo propertiesofcarryvaluetransformation AT birendrakumarnayak propertiesofcarryvaluetransformation |