Chapter 4
Logic Gates and Boolean
Algebra
Introduction
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

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 EXNOR.
Switch S1 AND Switch S2 must be
closed to light the lamp
Switch S1 OR Switch S2 (or both of
them) 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
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OR Gate
Logic Gates and Circuit Diagrams
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AND 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 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
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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
AB(A + B’C +C)
Solution:
ABA + ABB’C + ABC
AB + 0 + ABC
AB + 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