chapter 4
DESCRIPTION
Chapter 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. - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 4Chapter 4
Logic Gates and Boolean Algebra
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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.
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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
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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.
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Logic Gates and Circuit Diagrams
OR Gate
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Logic Gates and Circuit Diagrams
AND GateAND Gate
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Logic Gates and Circuit Diagrams
NOT Gate
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Logic Gates and Circuit Diagrams
NOR Gate
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Logic Gates and Circuit Diagrams
NAND Gate
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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
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Describing Logic Circuits Algebraically
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Describing Logic Circuits Algebraically
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Evaluating Logic Circuit Outputs
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Evaluating Logic Circuit Outputs
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Determining Output Level from a Diagram
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Implementing Circuits From Boolean Expression
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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.
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Boolean Algebra
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Boolean Algebra
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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
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Boolean Algebra
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Universality of NAND & NOR Gates
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Universality of NAND & NOR Gates
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Alternate Logic Gate Representations
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Forms and Definitions of Boolean Expressions
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Product of Sums Representation
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Disjunctive Normal Form
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Disjunctive Normal Form
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Disjunctive Normal Form
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Disjunctive Normal Form
Using truth tables, convert this expression into a sum of minterms