Natural and Efficient Subtraction Operation in Carry Value Transformation (CVT)-Exclusive OR (XOR) Paradigm

Das, Jayanta Kumar; Choudhury, Pabitra Pal; Arora, Ayesha

doi:10.1007/978-3-319-49001-4_10

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2017

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“…Later in 2014, a special class of one dimensional Integral Value Transformation (called Collatz-like) is studied in [Hassan, 2015]. A couple of other works are done on IVTs and their applications in arithmetic logical circuit design and in Biology [Pal et al, 2012;Choudhury et al, 2009bChoudhury et al, , 2008Choudhury et al, , 2011Das et al, 2016;Hassan et al, 2012]. In this present article, an attempt has been initiated to understand the discrete dynamics of Collatz-like including other two dimensional Integral Value Transformations.…”

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confidence: 94%

Two Dimensional Discrete Dynamics of Integral Value Transformations

Das,

Sahoo,

Hassan

et al. 2017

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A notion of Integral Value Transformations (IVTs) is defined over N×N using pair of two variable Boolean functions. The dynamics of the IVTs over N×N is studied from algebraic perspective. It is seen that the dynamics of the IVTs solely depend on the dynamics (state transition diagram) of the pair of two variable Boolean functions. A set of sixteen Collatz-like IVTs ae identified. Also, the dynamical system of IVTs having attractor with one (Non-Collatz-like) two, three and four cycles are studied.

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