EEEE-120_Lecture 2_logic Circuits_1.pdf

7/24/2019 EEEE-120_Lecture 2_logic Circuits_1.pdf

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RIT DubaiDigital Systems I EEEE-120

Introduction to Logic

CircuitsLamia Tchoketch Kebir

Spring 2016

Based on Stephen Brown and Zvonko Vranesic,

Fundamentals of Digital Logic with VHDL Design

McGraw-Hill, 3rdEdition

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ObjectivesO Logic functions and circuits

O Boolean Algebra

O Logic gates and synthesis of simple circuits.

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IntroductionO The study of logic circuits is motivated

mostly by their use in digital computers.

O Logic circuits perform operations on digitalsignals and are usually implemented as

electronic circuits where the signal values

are restricted to few discrete values.

O

In binary logic circuits there are only twovalues, 0 and 1.

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Variables and Functions

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Symbol for a switch

Switch open: x = 0, Switch closed: x = 1

The simplest binary element is a switch that has two states.

Input variable: x

Input: x,

Output: y = F(x)

state of the

light F(x) = x.


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Variables and Functions

x y

0 0

1 1

x1 x2 y

0 0 00 1 0

1 0 0

1 1 1

x1 x2 y

0 0 0

0 1 1

1 0 1

1 1 15


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Inversionx y

0 1

1 0

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Truth Tables

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A truth table shows the output of the function for all the combinations

of the inputs


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Logic Gates and Networks

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Analysis of a Logic Network

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Determine the function performed by the following network (analysis)


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Analysis of a Logic Network

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Functionally Equivalent Networks

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Determine the function performed by the following two networks


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Boolean Algebra

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DeMorgansTheorem

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Prove DeMorganstheorem by induction (using truth tables)


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DeMorgansTheorem

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Example 1

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Example 1

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Example 2


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Example 3


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Venn Diagram representation

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Verification of the distributive

property

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Verify

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Precedence of OperationsO Operations in a logic expression must be performed

in the order: Parentheses, NOT, AND, and then OR

O Example:

O In ordinary arithmetic, the same precedence holds

Multiplication AND

AdditionOR

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EEEE-120_Lecture 2_logic Circuits_1.pdf

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