Multi-Number CVT-XOR Arithmetic Operations in any Base System and its Significant Properties

TL;DR

This paper extends the CVT-XOR arithmetic model to multiple non-negative integers in any base system, exploring its properties and designing a parallel adder circuit using cellular automata.

Contribution

It generalizes CVT-XOR operations to multiple integers in any base and studies their properties, enabling the design of a parallel adder circuit.

Findings

Extended CVT-XOR to multiple integers in any base.

Identified key properties of multi-integer CVT-XOR operations.

Designed a parallel adder circuit using cellular automata.

Abstract

Carry Value Transformation (CVT) is a model of discrete dynamical system which is one special case of Integral Value Transformations (IVTs). Earlier in [5] it has been proved that sum of two non-negative integers is equal to the sum of their CVT and XOR values in any base 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 that 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.