Chapter 4Chapter 4

Logic Gates and Boolean Algebra

Introduction

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

Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX-NOR.

Switch S1 OR Switch S2 (or both of them) must be closed

to light the lamp

Switch S1 AND Switch S2 must be closed to light the

lamp

Truth Table

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

OR Gate

Logic Gates and Circuit Diagrams

AND GateAND Gate

Logic Gates and Circuit Diagrams

NOT Gate

Logic Gates and Circuit Diagrams

NOR Gate

Logic Gates and Circuit Diagrams

NAND Gate

Logic Gates and Circuit Diagrams

EX-OR gateThe '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 gateis 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

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

AB(A + B’C +C)Solution:

ABA + ABB’C + ABCAB + 0 + ABCAB + ABCAB

(A’B(’)A+B)Solution:

(A + B( )’A + B)AA + B’A + AB + B’BA + B’A + ABA + ABA

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