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Representations of Multiple-Valued Logic Functions
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Compared to binary switching functions, multiple-valued functions offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible.
Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools.
The book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts, various related decision diagrams. Three valued, or ternary functions, are traditionally used as the first extension from the binary case. A good feature of theirs is that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favorable for ternary functions.
Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easily coded by binary values and realized with two-stable state circuits. At the same time, there is much considerable advent in design of four valued logic circuits, than for other p-valued functions.
Therefore, the book is written in a hands-on approach, such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and interconnections among them.
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Morgan & Claypool Publishers; June 2012
170 pages; ISBN 9781608459438
Read online, or download in secure PDF format
170 pages; ISBN 9781608459438
Read online, or download in secure PDF format
More from this author
Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design2005US$ 117.00262 pages
Subject categories
- Academic > Mathematics > General > Logic, Symbolic and mathematical
- Academic > Mathematics > General > Nonclassical mathematical logic
- Academic > Mathematics > General > Many-valued logic
- Academic > Mathematics > Instruments and machines
- Academic > Mathematics > Analytic mechanics
- Academic > Logic > Nonclassical mathematical logic
- Academic > Logic > Many-valued logic
- Academic > Computer Science
- Technology > Electronics > Circuits
ISBNs
1608459438
9781608459421
9781608459438