期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2012
卷号：2012
DOI：10.1155/2012/174372
出版社：Hindawi Publishing Corporation
摘要：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.
