Multi-number CVT-XOR Arithmetic Operations in Any Base System and Its Significant Properties

摘要

Carry Value Transformation (CVT) is one of the modified structures of Integral Value Transformations (IVTs) and coming under the category of discrete dynamical system. Earlier in [5] it has been proved that the addition of two non-negative integers is equal to the addition of their CVT values and XOR values and is true in any base of the number system. In the present study, this phenomenon is extended to perform CVT and XOR operations for many non-negative integers in any base system. To achieve this both the definition of CVT and XOR are modified over the set of multiple integers instead of two. Also some important properties of these operations have been studied. With the help of cellular automata the adder circuit designed in [14] on using CVT-XOR recurrence formula is used to design a parallel adder circuit for multiple numbers in binary number system.