Good book on boolean algebra and logic for more advanced students
Posted by calvinnme on 5/28/2006
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.