Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook

Decision diagram (DD) techniques are very popular in the electronic design automation (EDA) of integrated circuits, and for good reason. They can accurately simulate logic design, can show where to make reductions in complexity, and can be easily modified to model different scenarios. Presenting DD techniques from an applied perspective, Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook provides a comprehensive, up-to-date collection of DD techniques. Experts with more than forty years of combined experience in both industrial and academic settings demonstrate how to apply the techniques to full advantage with more than 400 examples and illustrations. Beginning with the fundamental theory, data structures, and logic underlying DD techniques, they explore a breadth of topics from arithmetic and word-level representations to spectral techniques and event-driven analysis. The book also includes abundant references to more detailed information and additional applications. Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook collects the theory, methods, and practical knowledge necessary to design more advanced circuits and places it at your fingertips in a single, concise reference.

Computers & Technology

Yanushkevich, Svetlana N.

Shmerko, Vlad P.

Stanković, Radomir S.

Miller, D. Michael

Computer Science

CRC-Press

Fundamentals of Switching Theory and Logic Design discusses the basics of switching theory and logic design from a slightly alternative point of view and also presents links between switching theory and related areas of signal processing and system theory. Switching theory is a branch of applied mathematic providing mathematical foundations for logic design, which can be considered as a part of digital system design concerning realizations of systems whose inputs and outputs are described by logic functions.

Fundamentals of Switching Theory and Logic Design: A Hands on Approach

Science & Math

Astola, Jaakko

Physics

Springer

This textbook is intended for those economic geologists who deal with the evaluation of deposits at an early stage of development. It offers rules for quick and easy calculations based on the application of approximate figures. Both students and field geologists will find a complete set of rules and methods enabling them to perform a quick initial evaluation of the ore deposit.

Fundamentals of Switching Theory and Logic Design

Earth Sciences

Discover applications of Fourier analysis on finite non-Abelian groups The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods. Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design examines aspects of Fourier analysis on finite non-Abelian groups and discusses different methods used to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as an example of discrete functions in engineering practice. Additionally, consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelian groups. A solid foundation of this complex topic is provided by beginning with a review of signals and their mathematical models and Fourier analysis. Next, the book examines recent achievements and discoveries in: <ul>
<li>Matrix interpretation of the fast Fourier transform</li> <li>Optimization of decision diagrams</li> <li>Functional expressions on quaternion groups</li> <li>Gibbs derivatives on finite groups</li> <li>Linear systems on finite non-Abelian groups</li> <li>Hilbert transform on finite groups</li> </ul>
Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups in compact representations of discrete functions and related tasks in signal processing and system design, including logic design. All chapters are self-contained, each with a list of references to facilitate the development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this is an excellent textbook for graduate-level students and researchers in signal processing, logic design, and system theory-as well as the more general topics of computer science and applied mathematics.

Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design

Moraga, Claudio

Networking & Cloud Computing

Wiley-IEEE Press

Spectral techniques facilitate the design and testing of today's increasingly complex digital devices There is heightened interest in spectral techniques for the design of digital devices dictated by ever increasing demands on technology that often cannot be met by classical approaches. Spectral methods provide a uniform and consistent theoretic environment for recent achievements in this area, which appear divergent in many other approaches. Spectral Logic and Its Applications for the Design of Digital Devices gives readers a foundation for further exploration of abstract harmonic analysis over finite groups in the analysis, design, and testing of digital devices. After an introduction, this book provides the essential mathematical background for discussing spectral methods. It then delves into spectral logic and its applications, covering: * Walsh, Haar, arithmetic transform, Reed-Muller transform for binary-valued functions and Vilenkin-Chrestenson transform, generalized Haar, and other related transforms for multiple-valued functions * Polynomial expressions and decision diagram representations for switching and multiple-value functions * Spectral analysis of Boolean functions * Spectral synthesis and optimization of combinational and sequential devices * Spectral methods in analysis and synthesis of reliable devices * Spectral techniques for testing computer hardware This is the authoritative reference for computer science and engineering professionals and researchers with an interest in spectral methods of representing discrete functions and related applications in the design and testing of digital devices. It is also an excellent text for graduate students in courses covering spectral logic and its applications.

Spectral Logic and Its Applications for the Design of Digital Devices

Karpovsky, Mark G.

Astola, Jaakko T.

Programming

Wiley-Interscience

Decision diagram (DD) techniques are very popular in the electronic design automation (EDA) of integrated circuits, and for good reason. They can accurately simulate logic design, can show where to make reductions in complexity, and can be easily modified to model different scenarios. Presenting DD techniques from an applied perspective, Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook provides a comprehensive, up-to-date collection of DD techniques. Experts with more than forty years of combined experience in both industrial and academic settings demonstrate how to apply the techniques to full advantage with more than 400 examples and illustrations. Beginning with the fundamental theory, data structures, and logic underlying DD techniques, they explore a breadth of topics from arithmetic and word-level representations to spectral techniques and event-driven analysis. The book also includes abundant references to more detailed information and additional applications. Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook collects the theory, methods, and practical knowledge necessary to design more advanced circuits and places it at your fingertips in a single, concise reference.

Compared to binary switching functions, the multiple-valued functions (MV) 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. 
 This 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. They have a good feature 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 favourable 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 easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other p-valued functions. 
 Therefore, this book is written using 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 the interconnections among them. 
 Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms

Representation of Multiple-Valued Logic Functions (Synthesis Lectures on Digital Circuits and Systems, 37)

Astola, Jaako T.

Morgan & Claypool Publishers

Bent Functions and Permutation Methods: Binary and Multiple-Valued Bent Functions (Synthesis Lectures on Engineering, Science, and Technology)

Stanković, Milena

Reference

Logic networks and automata are facets of digital systems. The change of the design of logic networks from skills and art into a scientific discipline was possible by the development of the underlying mathematical theory called the Switching Theory. The fundamentals of this theory come from the attempts towards an algebraic description of laws of thoughts presented in the works by George J. Boole and the works on logic by Augustus De Morgan.
As often the case in engineering, when the importance of a problem and the need for solving it reach certain limits, the solutions are searched by many scholars in different parts of the word, simultaneously or at about the same time, however, quite independently and often unaware of the work by other scholars. The formulation and rise of Switching Theory is such an example. 
This book presents a brief account of the developments of Switching Theory and highlights some less known facts in the history of it. The readers will find the book a fresh look into the development of the field revealing how difficult it has been to arrive at many of the concepts that we now consider obvious . Researchers in the history or philosophy of computing will find this book a valuable source of information that complements the standard presentations of the topic.

From Boolean Logic to Switching Circuits and Automata: Towards Modern Information Technology (Studies in Computational Intelligence, 335)

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