Properties of Carry Value Transformation
2012 ◽
Vol 2012
◽
pp. 1-10
◽
Keyword(s):
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 eitherCVT=0orXOR=0does 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 onZ×Zwhich divides the CV table into disjoint equivalence classes.
2012 ◽
Vol 26
(25)
◽
pp. 1246006
1989 ◽
Vol 41
(5)
◽
pp. 830-854
◽
1958 ◽
Vol 13
◽
pp. 135-156
◽
Keyword(s):
Keyword(s):
Keyword(s):
2009 ◽
Vol 15
(2)
◽
pp. 145-168
◽
1980 ◽
Vol 77
(1)
◽
pp. 215-224
◽
Keyword(s):
2007 ◽
Vol 17
(12)
◽
pp. 4463-4469
◽