Chapter 1: Foundations of Digital Design

Introduction

Digital design is the backbone of modern computing, enabling the creation of hardware systems that process and store information efficiently. This chapter introduces the fundamental concepts necessary to understand and design digital circuits.

Topics Covered:

• Number Systems and Representations: Understanding binary, octal, hexadecimal, and decimal systems.
• Boolean Algebra and Logic Gates: Basic logic operations, De Morgan’s Theorems, and gate-level design.
• Truth Tables and Logic Expressions: Methods for representing and simplifying logic functions.
• Sum of Products (SOP) and Product of Sums (POS): Standard forms of Boolean functions.
• Karnaugh Maps and Simplification Techniques: Graphical methods for logic minimization.
• Binary Arithmetic and Two’s Complement: Addition, subtraction, and representation of signed and unsigned numbers.

Learning Objectives:

By the end of this chapter, you will:

• Understand different number systems and their applications in digital design.
• Apply Boolean algebra and logic gates to design basic digital circuits.
• Use truth tables and logic expressions to analyze combinational circuits.
• Simplify logic functions using Karnaugh Maps and algebraic techniques.
• Perform binary arithmetic operations, including signed and unsigned calculations.

This chapter serves as the foundation for combinational and sequential circuit design, covered in later chapters of the textbook.