Overview
- A unifying math/engineering approach to the basic computer functions: - combinational logic, arithmetic and state machines
- Boolean logic spectral analysis yields planar mapping in Silicon VLSI technology
- A residue-and-carry method allows proving the conjectures of Fermat and Goldbach
- New binary coded log-arithmetic, and VLSI implementation, are described
- The five basic state machines (BSM) are derived via their sequential closure
- State-machine synthesis as coupled BSM network by a new semigroup method
- Includes supplementary material: sn.pub/extras
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Associative Digital Network Theory is intended for researchers at industrial laboratories,
teachers and students at technical universities, in electrical engineering, computer science and applied mathematics departments, interested in new developments of modeling and designing digital networks (DN: state machines, sequential and combinational logic) in general, as a combined math/engineering discipline. As background an undergraduate level of modern applied algebra (Birkhoff-Bartee: Modern Applied Algebra - 1970, and Hartmanis-Stearns: Algebraic Structure of Sequential Machines - 1970) will suffice.
Essential concepts and their engineering interpretation are introduced in a practical fashion with examples. The motivation in essence is: the importance of the unifying associative algebra of function composition (viz. semigoup theory) for the practical characterisation of the three main functions in computers, namely sequential logic (state-machines), arithmetic and combinational (Boolean) logic.
Reviews
From the reviews:
"Benschop develops this thesis in an idiosyncratic fashion, reinforced by a long career of practical experience. This book may well be an important historical document, also useful for seminars … . There are profuse illustrations in classic number theory, as well as claims that the outlook sheds new light on classic problems such as those of Fermat and Goldbach, interpreted as machines. … it makes for an interesting book." (Harvey Cohn, ACM Computing Reviews, August, 2009)
“The book presents new ways for modeling digital networks (state machines, sequential and combinational logic). It contains applications for known principles of the discrete mathematics. … book also presents new ideas on the finite additive number theory and a binary logarithmetic microprocessor. This book can be very useful for students and professors and also for researchers interested in the digital network theory. It covers a lot of fields, ranging from electrical engineering to computer science and applied mathematics.” (Eleonor Ciurea, Zentralblatt MATH, Vol. 1169, 2009)
About the author
Bibliographic Information
Book Title: Associative Digital Network Theory
Book Subtitle: An Associative Algebra Approach to Logic, Arithmetic and State Machines
Authors: Nico F. Benschop
DOI: https://doi.org/10.1007/978-1-4020-9865-9
Publisher: Springer Dordrecht
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer Science+Business Media B.V. 2009
Edition Number: 1
Number of Pages: XII, 180
Topics: Computer Communication Networks, Communications Engineering, Networks, Logic Design, General Algebraic Systems, Discrete Mathematics in Computer Science, Mathematical Logic and Formal Languages