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

Jaakko Astola, Radomir S. Stankovic

  • 出版商: Springer
  • 出版日期: 2006-03-07
  • 售價: $1,580
  • 貴賓價: 9.8$1,548
  • 語言: 英文
  • 頁數: 342
  • 裝訂: Hardcover
  • ISBN: 0387285938
  • ISBN-13: 9780387285931
  • 相關分類: 邏輯設計 Logic-design
  • 下單後立即進貨 (約5~7天)

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商品描述

Description

Switching theory and logic design provide mathematical foundations and tools for digital system design that is an essential part in the research and development in almost all areas of modern technology. The vast complexity of modern digital systems implies that they can only be handled by computer aided design tools that are built on sophisticated mathematical models. Fundamentals of Switching Theory and Logic Design is aimed at providing an accessible introduction to these mathematical techniques that underlie the design tools and that are necessary for understanding their capabilities and limitations.

As is typical to many disciplines a high level of abstraction enables a unified treatment of many methodologies and techniques as well as provides a deep understanding of the subject in general. The drawback is that without a hands-on touch on the details it is difficult to develop an intuitive understanding of the techniques. We try to combine these views by providing hands-on examples on the techniques while binding these to the more general theory that is developed in parallel. For instance, the use of vector spaces and group theory unifies the spectral (Fourier-like) interpretation of polynomial, and graphic (decision diagrams) representations of logic functions, as well as provides new methods for optimization of logic functions.

Consequently, Fundamentals of Switching Theory and Logic Design discusses the fundamentals 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. It also covers the core topics recommended in IEEE/ACM curricula for teaching and study in this area. Further, it contains several elective sections discussing topics for further research work in this area

 

Table of contents

Preface. Acronyms.

1. SETS, RELATIONS, AND FUNCTIONS. 1. Sets. 2. Relations. 3. Functions. 4. Representations of Logic Functions. 5. Factored Expressions. 6. Exercises and Problems.

2. ALGEBRAIC STRUCTURES FOR LOGIC DESIGN. 1. Algebraic Structure. 2. Finite Groups. 3. Finite Rings. 4. Finite Fields. 5. Homomorphisms. 6. Matrices. 7. Vector spaces. 8. Algebra. 9. Boolean Algebra. 10. Graphs. 11. Exercises and Problems.

3. FUNCTIONAL EXPRESSIONS FOR SWITCHING FUNCTIONS. 1. Shannon Expansion Rule. 2. Reed-Muller Expansion Rules. 3. Fast Algorithms for Calculation of RM-expressions. 4. Negative Davio Expression. 5. Fixed Polarity Reed-Muller Expressions. 6. Algebraic Structures for Reed-Muller Expressions. 7. Interpretation of Reed-Muller Expressions. 8 Kronecker Expressions. 9. Word-Level Expressions. 10. Walsh Expressions. 11. Walsh Functions and Switching Variables. 12. Walsh Series. 13. Relationships Among Expressions. 14. Generalizations to Multiple-Valued Functions. 15. Exercises and Problems.

4. DECISION DIAGRAMS FOR REPRESENTATION OF SWITCHING FUNCTIONS. 1. Decision Diagrams. 2. Decision Diagrams over Groups. 3. Construction of Decision Diagrams. 4. Shared Decision Diagrams. 5. Multi-terminal binary decision diagrams. 6. Functional Decision Diagrams. 7. Kronecker decision diagrams. 8. Pseudo-Kronecker decision diagrams. 9. Spectral Interpretation of Decision Diagrams. 10. Reduction of Decision Diagrams. 11. Exercises and Problems.

5. CLASSIFICATION OF SWITCHING FUNCTIONS. 1. NPN-classification. 2. SD-Classification. 3. LP-classification. 4. Universal Logic Modules. 5. Exercises and Problems.

6. SYNTHESIS WITH MULTIPLEXERS. 1. Synthesis with Multiplexers. 2. Applications of Multiplexers. 3. Demultiplexers. 4. Synthesis with Demultiplexers. 5. Applications of Demultiplexers. 6. Exercises and Problems.

7. REALIZATIONS WITH ROM. 1. Realizations with ROM. 2. Two-level Addressing in ROM Realizations. 3. Characteristics of Realizations with ROM. 4. Exercises and Problems.

8. REALIZATIONS WITH PROGRAMMABLE LOGIC ARRAYS. 1. Realizations with PLA. 2. The optimization of PLA. 3. Two-level Addressing of PLA. 4. Folding of PLA. 5. Minimization of PLA by Characteristic Functions. 6. Exercises and Problems.

9. UNIVERSAL CELLULAR ARRAYS. 1. Features of Universal Cellular Arrays. 2. Realizations with Universal Cellular Arrays. 3. Synthesis with Macro Cells. 4. Exercises and Problems.

10. FIELD PROGRAMMABLE LOGIC ARRAYS. 1. Synthesis with FPGAs. 2. Synthesis with Antifuse-Based FPGAs. 3. Synthesis with LUT-FPGAs. 4. Exercises and Problems.

11. BOOLEAN DIFFERENCE AND APPLICATIONS IN TESTING LOGIC NETWORKS. 1. Boolean Difference. 2. Properties of the Boolean Difference. 3. Calculation of the Boolean Difference. 4. Boolean Difference in Testing Logic Networks. 5. Easily Testable Logic Networks. 6. Easily Testable Realizations from PPRM-expressions. 7. Easily Testable Realizations from GRM-expressions. 8. Exercises and Problems.

12. SEQUENTIAL NETWORKS. 1. Basic Sequential Machines. 2. State Tables. 3. Conversion of Sequential Machines. 4. Minimization of States. 5. Incompletely Specified Machines. 6. State Assignment. 7. Decomposition of Sequential Machines. 8. Exercises and Problems.

13. REALIZATION OF SEQUENTIAL NETWORKS. 1. Memory Elements. 2. Synthesis of Sequential Networks. 3. Realization of Binary Sequential Machines. 4. Realization of Synchronous Sequential Machines. 5. Pulse Mode Sequential Networks. 6. Asynchronous Sequential Networks. 7. Races and Hazards. 8. Exercises and Problems.

References. Index

商品描述(中文翻譯)

描述

切換理論和邏輯設計提供了數學基礎和工具,用於數字系統設計,這是現代技術幾乎所有領域的研究和開發的重要組成部分。現代數字系統的巨大複雜性意味著它們只能通過建立在複雜數學模型上的計算機輔助設計工具來處理。《切換理論和邏輯設計基礎》旨在提供對這些數學技術的可理解介紹,這些技術是設計工具的基礎,也是理解其能力和限制所必需的。

與許多學科一樣,高度抽象的水平使得可以統一處理許多方法和技術,並提供對該主題的深入理解。缺點是,如果沒有對細節進行實踐性的觸摸,很難發展對技術的直觀理解。我們試圖通過提供對技術的實踐性示例,同時將其與平行發展的更一般理論相結合,來結合這些觀點。例如,使用向量空間和群論統一了多項式的頻譜(類似傅立葉)解釋和邏輯函數的圖形(決策圖)表示,並提供了優化邏輯函數的新方法。

因此,《切換理論和邏輯設計基礎》從稍微不同的角度討論了切換理論和邏輯設計的基礎,並介紹了切換理論與信號處理和系統理論相關領域之間的聯繫。它還涵蓋了IEEE/ACM課程中推薦的核心主題,以供教學和研究使用。此外,它還包含了幾個選修部分,討論了這一領域的進一步研究工作的主題。

目錄

前言。縮寫。

1. 集合、關係和函數。1. 集合。2. 關係。3. 函數。4. 邏輯函數的表示。5. 分解表達式。6. 練習和問題。

2. 邏輯設計的代數結構。1. 代數結構。2. 有限群。3. 有限環。4. 有限域。5. 同態。6. 矩陣。7. 向量空間。8. 代數。9. 布爾代數。10. 圖形。11. 練習和問題。

3. 切換函數的功能表達式。1. Shannon展開規則。2. Reed-Muller展開規則。3. 快速計算RM表達式的算法。4. 負Davio表達式。5. 固定極性的Reed-Muller表達式。6. Reed-Muller表達式的代數結構。7. Reed-Muller表達式的解釋。8. Kronecker表達式。9. 字級表達式。10. Walsh表達式。11. Walsh函數和切換變量。12. Walsh序列。13. 表達式之間的關係。14. 對多值函數的推廣。15. 練習和問題。

4. 切換函數的決策圖表示。1. 決策圖。2. 群上的決策圖。3. 決策圖的構造。4. 共享決策圖。5. 多終端二進制決策圖。6. 功能性決策圖。7. Kronecker決策圖。8. 偽Kronecker決策圖。9. 決策圖的頻譜解釋。10. 決策圖的簡化。11. 練習和問題。