Ch 6. Boolean Algebra and Combinatorial Circuits
Learning Objectives
By the end of this chapter, students should be able to:
- Analyze and design combinational logic circuits using logic gates, truth tables, and Boolean expressions.
- Simplify and manipulate Boolean expressions using Boolean algebra laws, including De Morgan’s laws.
- Represent Boolean functions with truth tables, SOP and POS forms, and implement efficient digital circuits.
- Compare and verify equivalent Boolean expressions and circuit designs.
In Chapters 1 and 2, you learned about binary number representation and arithmetic, which are the foundations of digital systems. In Chapter 3, you learned about logic operations such as conjunction, disjunction, and negation. This chapter combines the two to introduce you to binary logic, the basis for how every decision is made in digital systems ranging from smartphones to traffic light controllers, using values of 0 or 1. First, you will explore how such decisions are implemented through combinatorial circuits, which compute outputs solely from their current inputs using logic gates such as AND, OR, and NOT. Following this, you will learn to interpret truth tables, translate Boolean expressions into circuits, and analyze designs.
The chapter then develops the mathematical framework behind these circuits through Boolean algebra, introducing fundamental laws that support the simplification and manipulation of logical expressions. Building on this foundation, you will study Boolean functions and learn methods for expressing them in forms such as Sum of Products or Product of Sums, leading to efficient circuit synthesis.
