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Schaum's Outline of Boolean Algebra and Switching Circuits

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This book is devoted to two separate and related topics: the theory of Boolean algebra and logic and also the synthesis and simplification of switching and logic circuits. This is a good book for students taking a course on digital logic that has more of a computer science or mathematics perspective rather than an electrical engineering viewpoint. There is no mention of gates or digital circuit building blocks of any kind in this outline. The treatment of switching and logic circuits is limited to the combinational circuits - those circuits whose outputs depend only on the present inputs.
Chapter 1 goes over the basics of boolean logic and the notation used in this outline. Chapter 2 discusses sets and their operations and extends boolean logic to sets of objects. Chapter 3 discusses Boolean algebra, which is a set B together with two binary operations, a singular operation, the two specific elements 0 and 1, and a set of axioms. Thus, in this chapter we are led more into the realm of mathematics than circuits with a good number of proofs as exercises. Chapter 4 abruptly changes course and discusses switching and logic circuits. Here, previous discussions of Boolean logic lead to the practical tasks of minimization and the finding of all prime implicants of a set. The final chapter changes course once again and discusses some advanced topics in Boolean algebra such as lattices, rings, and m-completeness.
Although no specific previous knowledge is really explicitly required to understand this material, I would say that working through the material I found that experience with mathematical proofs, set theory, and oddly enough, abstract algebra were all very advantageous in understanding this outline. It is one of the better written Schaum's outline in that the theory is very well explained. I would recommend it for the more mathematically inclined who are interested in digital logic.

This is one of the elements of the Schaum's set that helped make my career. When I was first starting out as a college instructor, I was a math major but had little experience in computer science. In order to quickly flesh out my skills so that I could teach discrete mathematics, I checked this book out of the library and started working the problems. Although my background in abstract algebra helped in my understanding of the theory, my real goal was to learn the applications to digital circuits.
This goal was satisfied, in a short time, I was able to cover digital circuits in the discrete class and a short time later, was able to teach a class in digital logic for computer science majors.

For those of you inclined to the theoretical aspects of computing, this book may be good revision. The first half of the book deals with set theory and then with Boolean algebra. The Boolean concepts should be easy to follow, and likewise with the problems presented to you here.

What is more challenging is the second half, dealing with switching circuits. You can see techniques that map from a logic circuit to its Boolean representation. And then the vital idea of a Karnaugh map, in order to simplify that representation. Digital circuit designers live for this stuff! Many problems to chew on. See how well you really understand the material.

You might look with askance on the publication date of 1970. 1970?! Moore had barely formulated his law a few years earlier. And Medium Scale Integration was the order of the day, perhaps, with the first microprocessor still under design. But the maths in this book still holds true now. In fact, it is even more relevant today. Because the circuits are orders of magnitude larger, so finding efficient means of circuit minimisation are more urgent. For that, you need a solid theoretical basis. And this book can test that understanding.