金沢大学理工研究域電子情報学

Akita Junichi

Iwabuchi Yuuki

Yuuki Iwabuchi

Junichi Akita

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Properties of “Planar Binary (Butchi Number)”

金沢大学融合研究域融合科学系 / 金沢大学理工研究域電子情報学

秋田 純一

Kanazawa University Repository for Academic Resources

Properties of "planar binary (butchi number)著者 Iwabuchi Yuuki, Akita Junichijournal orpublication titleLecture Notes in Computer Science (includingsubseries Lecture Notes in ArtificialIntelligence and Lecture Notes inBioinformatics)number 6079 LNCSpage range 190year 2010-01-01URL http://hdl.handle.net/2297/28326doi: 10.1007/978-3-642-13523-1_23Properties of \Planar Binary (Butchi Number)"Yuuki Iwabuchi, Junichi AkitaDivision of Electrical Engineering and Computer Science, Kanazawa universitybutchi@merl.jp,akita@is.t.kanazawa-u.ac.jp1 IntroductionConventional binary numbers has the carry rule of leftward propagation in lineararray. In this paper, we propose the number representation with the carry ruleof both leftward and upward propagations in planar array, which we call \planarbinary (Butchi number)," and we describe their properties.2 Property of \Planar Binary"In the procedure of increment in \Butch number," the carry paths branch forboth leftward and upward at the reversing bit accroding to propergating carries.The arithmetical operations of addition and multiplication can be dened for theButchi number, that satisfy both the commutative law and the distributive law.The Butchi number representations for large natural numbers generally haverecursive triangles shapes. The Butchi number representation can be consideredas the extension of the binary number in one dimentional representation for twodimentional representaion. The possibility of the operation representation withsimple rule in two dimentional domain will be discussed in our future works.363 364(a) (b)Fig. 1. Examples of Planer Binary's property. (a)Representation of 40000 and(b)Incremental Operation.

Properties of "planar binary (butchi number)

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Properties of “Planar Binary (Butchi Number)”

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