Abstract
Carry value transformation (CVT) and Exclusive OR (XOR) operations on two non-negative integers have been defined previously in several articles. In this paper, the definition of CVT and XOR operations are extended from non-negative integer to integer domain. Thereafter various cases of integer pairs towards their convergence behaviour are thoroughly discussed. Our analyses through the convergence behavior of integer pairs are easily directed to capture the natural subtraction operation in this paradigm by representing negative integer in 2’s complement form. The average time complexity of the addition/subtraction operation is seen to be highly competitive in any bulk computation in real life scenario. In other words, in the event of bulk addition/subtraction operation to be performed, the average time complexity is seen to be highly efficient.
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Acknowledgments
Authors would like to thank Dr. Sudhakar Sahoo (Institute of Mathematics and Applications, Bhubaneswar-751029, India) for his valuable suggestion.
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Das, J.K., Pal Choudhury, P., Arora, A. (2016). Natural and Efficient Subtraction Operation in Carry Value Transformation (CVT)-Exclusive OR (XOR) Paradigm. In: Martín-Vide, C., Mizuki, T., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2016. Lecture Notes in Computer Science(), vol 10071. Springer, Cham. https://doi.org/10.1007/978-3-319-49001-4_10
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