Topics in Engineering Logic

International Series of Monographs on Electronics and Instrumentation

1st Edition - January 1, 1962
Author: Morton Nadler
Editors: D.W. Fry, W.A. Higinbotham
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 8 4 6 8 - 5

Topics in Engineering Logic contains the lectures given at the Indian Statistical Institute in Calcutta, India, during the Spring of 1959. The lectures focus on a variety of topics… Read more

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Topics in Engineering Logic contains the lectures given at the Indian Statistical Institute in Calcutta, India, during the Spring of 1959. The lectures focus on a variety of topics related to engineering logic, including the use of the logical matrix as an auxiliary to the construction of various types of codes. Elementary logical circuits for synchronous systems are also considered, with emphasis on "two-wire" systems based on static flip-flops and having various phase structures. Comprised of seven chapters, this volume begins with an introduction to the logical matrix, a form of representation of logical functions that permits rapid and clear solution of varied problems in logical design. The discussion then turns to elementary logical circuits for synchronous systems and their physical properties, with particular reference to contacts, diodes, and transistors as well as phase structures and diode-gated flip-flops for single-phase and two-phase applications. Subsequent chapters deal with a graphical approach based on the logical matrix as a method for reducing the canonic form to the two-level minimal form; codes and matrices; operational circuits; and the question of increasing reliability through structural redundance. The book concludes with several typical logical design problems, including a drum-indexing circuit and a series-parallel decimal multiplier. This monograph will be of interest to engineers.

Preface

Chapter I. Introduction: The Logical Matrix

1. The Logical Variable

2. Logical Functions

3. The Logical Matrix

4. Operations on Logical Matrices

(a) Complementation of a Function

(b) Addition of Two Functions

(c) Multiplication of Two Functions

(d) Extension to Further Variables

(e) Transformation of Variables

(f) Function Rotation

(g) Expansion About a Subset of Variables

5. Adjacency and k-cells, Contact Grids

6. The Second Canonic Form

7. Symmetric Functions

8. Other Applications of the Logical Matrix

9. Multi-Valued Logic

10. The Connexion Matrix

Summary

Chapter II. Physical Considerations: Elementary Logical Circuits for Synchronous Systems

1. Contacts, Diodes and Transistors

2. “Complete” Logical Elements

3. Phase Structures

4. Diode-Gated Flip-Flops for Single-Phase and Two-Phase Application

5. Transistor Gates for Single-Phase and Two-Phase Logical Circuits

6. Transistor Gates for Direct-Coupled Logical Circuits

7. Interconnexion of Modes

Summary

Chapter III. The Minimal Form

1. Introductory Remarks

2. The Configuration Code

3. Redundancies and Operation Counts

4. Preliminary Definitions

5. Preparation of the Matrix for Minimization

6. Choice of k-cells: The First Rule

7. Choice of k-cells: The Second Rule

8. Concrete Gate Synthesis

9. Switching Functions for the Case where the Output Variable Enters into the Function

Summary

Chapter IV. Codes and Matrices

1. Introduction

2. Hamming-Distance Codes

3. Decimal Codes

4. Shift-Register Codes

5. Commaless Codes

Summary

Chapter V. Operational Circuits

1. Circuit Complexity

2. The Operational Circuit

3. Delay, Output Rate and Critical Functions

4. Upper Bound on the Complexity of Maximally Simplified Critical Functions

5. Critical Functions and Sequential Circuits

6. The Construction of Auxiliary Functions

Summary

Chapter VI. Structural Redundance

1. Failure Rates

2. Marginal Checking

3. Microredundance

4. Maximum Redundance

Appendix 1 : Statistics of Microredundance (Doubling)

Appendix 2: Statistics of Maximum Redundance

Summary

Chapter VII. Examples

1. Drum-Indexing Circuit

2. Tape-to-Drum Buffer Register

3. Bi-Directional Decimal Counter

4. Series-Parallel Decimal Multiplier

List of References

Index