Chapter 4 Logic Gates and Boolean Algebra Introduction

Chapter 4 Logic Gates and Boolean Algebra

Introduction n Logic gates are the actual physical implementations of the logical operators. These gates form the basic building blocks for all digital logic circuits. Logic gates process signals which represent true or false.

Introduction n Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EXNOR. Switch S 1 AND Switch S 2 must be closed to light the lamp Switch S 1 OR Switch S 2 (or both of them) must be closed to light the lamp

Truth Table n A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.

Logic Gates and Circuit Diagrams n OR Gate

Logic Gates and Circuit Diagrams n AND Gate

Logic Gates and Circuit Diagrams n NOT Gate

Logic Gates and Circuit Diagrams n NOR Gate

Logic Gates and Circuit Diagrams n NAND Gate

Logic Gates and Circuit Diagrams n EX-OR gate The 'Exclusive-OR' gate is a circuit which will give a high output if either but not both, of its two inputs are high. § EX-NOR gate is The inversion of EX-OR Gate

Describing Logic Circuits Algebraically

Describing Logic Circuits Algebraically

Evaluating Logic Circuit Outputs

Evaluating Logic Circuit Outputs

Determining Output Level from a Diagram

Implementing Circuits From Boolean Expression

Boolean Algebra n n n Simplification of logical circuits. One tool to reduce logical expressions is the mathematics of logical expressions. The rules of Boolean Algebra are simple and straight-forward, and can be applied to any logical expression.

Boolean Algebra

Boolean Algebra

Boolean Algebra (A’B)’(A+B) Solution: (A + B’) (A + B) AA + B’A + AB + B’B A + B’A + AB A AB(A + B’C +C) Solution: ABA + ABB’C + ABC AB + 0 + ABC AB

Boolean Algebra

Universality of NAND & NOR Gates

Universality of NAND & NOR Gates

Alternate Logic Gate Representations

Forms and Definitions of Boolean Expressions

Product of Sums Representation

Disjunctive Normal Form

Disjunctive Normal Form

Disjunctive Normal Form

Disjunctive Normal Form Using truth tables, convert this expression into a sum of minterms