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DSYS1 - Module 2

Introduction to Logic Gates

Study Unit 1

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After completing this study unit you should:

Be Able to demonstrate understanding and application of the logic operators and gates

Be able to demonstrate understanding and application of Inverter, AND gate & OR gate

Outcomes


The Distinctive Shape Logic Symbol For The Inverter Is Shown Below

Inputs ► Left Of Shape; Outputs ► To Right

The Inverter


Inverter Symbols

The Rectangular Outline Symbol For The Inverter is shown below

These Are Used In Many Publications

The Inverter


Rectangular Inverter Symbols

1 1

Negation Indicator “O” Indicates Inversion On That Input Or Output

“O” Means 0 Is The Active Or Asserted Input / Output

The “Triangle” Symbol Used For Rectangular Symbols

Negation Indicators


Truth Table ► Shows The Output Of A Logic Gate Or Circuit For All Possible Inputs Combinations

Inverter Truth Table


in out

Input OutputLOW (0) HIGH(1)HIGH(1) LOW(0)

Inverter Truth Table

Timing Diagram – Shows Input And Output Waveforms In Relation To One Another In Time

Inverter Timing Diagram


Inverter Timing Diagram

Input

Output

Boolean Algebra Is Used To Mathematically Describe A Logic Gate Or Circuit

Variables Are Used In These Equations And Can Have A Value Of 0 Or 1

Variable Used Are: A, B, C … For Inputs And X, Y, Z, Q For Outputs

Boolean Algebra


The Compliment Of A Variable Is Equal To The Inverse Of The Variable◦ (Variable=1 ► Compliment Of The Variable =0)

Inverter Expression


A X

AX :Expression Boolean

Inverters May Be Used To Derive The 1’s Compliment Of A Binary Number◦ 74LS04 (Hex Inverter)

Inverter Application


1 0 1 1 Binary Number

0 1 0 0 1’s Compliment

Logic Gate ► Circuit That Performs A Basic Logic Operation

AND Gate ► Has Two Or More Inputs And A Single Output

The AND Gate


Distinctive Shape

Rectangular Outline

&

AND Gate ► Produces A HIGH Output Only If All Its Inputs Are HIGH, Otherwise It Puts Out LOW

AND Gate Operation


00

0 10

0

01

0 11

1

For n Input-variables There Are 2n Possible Input Combinations

AND Gate Truth Table


AB

X

A B X0 0 00 1 01 0 01 1 1

2-Input AND Truth Table

Complete The Truth Table For The 3-Input AND Gate Below

AND Gate Truth Table


A B C X0 0 0 00 0 1 00 1 0 00 1 1 01 0 0 01 0 1 01 1 0 01 1 1 1AND Gate Truth

Table

ABC

X

In Majority Of Applications The Inputs To A Gate Are Not Static Levels But Changing Waveforms

Such Waveforms Are Broken Down Into “Static Sections” And Then The Truth Table Can Be Applied To These Sections

Pulsed Gate Operation


Sections that are all HIGH => HIGH out

Pulsed AND Gate Operation


B

A

X

AB

X

Complete The Timing Diagram Below

AND Waveform Exercise


B

A

X

ABC

X

C

AND ► Boolean Multiplication◦ 0 · 0 = 0◦ 0 · 1 = 0◦ 1 · 0 = 0◦ 1 · 1 = 1

X = A · B

◦ 74LS08 (Quad 2-Input) 74LS11 (Triple 3-Input)

AND Expression


AB

X

AND Gate Is Commonly Use To Enable Signals To Pass From One Point To Another Or At Times To Inhibit Them ◦ See Frequency Counter & Seat Belt Alarm

AND Gate Application


0 01

Frequency Counter Application Example:

AND Gate Application …

Seat Belt Alarm Application Example:

AND Gate Application …

OR Gate ► Has Two Or More Inputs And A Single Output

The OR Gate

22

Rectangular Outline

1

Distinctive Shape

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OR Gate – Produces A HIGH Output If Any Of Its Inputs Are HIGH, And Only Puts Out A LOW All The Inputs Are LOW

The OR Gate

23

00

0 10

1

01

1 11

1

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OR Gate Truth Table

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A B X0 0 00 1 11 0 11 1 1

2-Input OR Truth Table

AB X

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Complete The Truth Table For The 3-Input OR Gate Below

OR Gate Truth Table

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A B C X0 0 0 00 0 1 10 1 0 10 1 1 11 0 0 11 0 1 11 1 0 11 1 1 1

OR Gate Truth Table

ABC

X

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Sections That Are All LOW ► LOW Out

OR Gate Waveforms

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B

A

X

AB

X

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Complete The Timing Diagram Below

OR Gate Waveform Exercise

27

B

A

X

C

ABC

X

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OR ► Boolean Addition (Not Same As Normal Addition)◦ 0 + 0 = 0◦ 0 + 1 = 1◦ 1 + 0 = 1◦ 1 + 1 = 1

X = A + B

OR Gate Expression

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Intrusion Alarm Systems Application Example:

◦ 74LS32 (Quad 2-Input)

OR Gate Applications

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