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LABORATORY11: Digital Logic Circuits. General Engineering Polytechnic University. Objectives Logic Functions Sample Problem Truth Table Boolean Equation Karnaugh Maps (K-maps) Simplified Boolean Equation Combinational Logic Circuit. Integrated Circuits (ICs) IC Identification

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LABORATORY11: Digital Logic Circuits

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Laboratory11 digital logic circuits l.jpg

LABORATORY11:Digital Logic Circuits

General Engineering

Polytechnic University


Overview l.jpg

Objectives

Logic Functions

Sample Problem

Truth Table

Boolean Equation

Karnaugh Maps (K-maps)

Simplified Boolean Equation

Combinational Logic Circuit

Integrated Circuits (ICs)

IC Identification

Digital Logic Trainer

Materials for Lab

Problem Statement

Procedure

Written Assignment

Written Topics

Recitation Topics

Closing

Overview


Objectives l.jpg

Objectives

  • Understand the functions of logic gates

  • Become familiar with digital circuits Use you new knowledge to design & implement a combinational logic circuit using the digital trainer


Logic functions l.jpg

Logic Functions

  • AND - “The all or nothing operator”

    • Output is high (1) only when ALL inputs are high (1)

  • OR gate - “The any or all operator”

    • Output is high (1) when at least ONE input is high (1)

  • NOT (INVERTER) operator

    • Output is opposite of input

    • Only one input and one output


Logic functions5 l.jpg

Logic Function

Logic Symbol

Boolean

Expression

Truth Table

Inputs Outputs

A

Y

AND

A

B

Y

B

A • B = Y

0

0

0

0

0

1

1

0

0

A

Y

1

1

1

A + B = Y

OR

B

0

0

0

0

1

1

1

0

1

1

A

Ā

1

1

NOT

A = Ā

0

1

1

0

Logic Functions


Sample problem l.jpg

Sample Problem

  • An ATM machine has three options, Print statement, Withdraw money, or Deposit Money

  • The ATM machine will charge you $1.00 if you:

    • Want to withdraw

    • Only want to print out your statement (no transactions at all)


Truth table l.jpg

A truth table is a table

that displays all possible

input combinations and

the resulting outputs.

INPUT OUTPUT

P = print C = charge

W = withdraw

D = deposit

0 = “do not” 0 = $0.00

1 = “do” 1 = $1.00

INPUTS

OUTPUT

W

D

C

P

0

0

0

0

0

0

1

0

0

1

0

1

1

0

1

1

1

1

0

0

1

0

1

0

1

1

0

1

1

1

1

1

Truth Table


Boolean equation l.jpg

INPUTS

OUTPUT

W

D

C

P

0

0

0

0

0

0

1

0

0

1

0

1

1

0

1

1

1

1

0

0

1

0

1

0

1

1

0

1

1

1

1

1

Boolean Equation

= PWD

Outputs with a value of “ONE” are kept

C=

+ PWD

+ PWD

+ PWD

+ PWD


Karnaugh maps k maps l.jpg

Place output ONE in corresponding boxes.

Circle neighboring ONES in multiples of 2, try to find the greatest amount of “neighbors” Only overlap circles as a last resort

Karnaugh Maps (K-maps)

C = PWD+ PWD+ PWD + PWD + PWD

PWD

PWD

PWD

0

0

0

1

1

1

1

0

P

W

P

W

P

W

P

W

1

1

1

0

D

1

1

1

D

_

Why can’t you switch PW and PW?

Why can’t you loop the three

adjacent 1s in the top row together?


Simplified boolean equation l.jpg

_ _

PWD

_

PWD

D

D

_

PWD

P

W

1

1

_ _

PWD

1

1

P

W

_

PWD

1

1

1

P

W

PWD

1

1

1

1

P

W

Simplified Boolean Equation

Opposite values cancel out

C =

W

_

+ PD


Combinational logic circuit l.jpg

W

C =

+

P

D

W

+

P

D

W

+

P

D

D

D

+

P

Combinational Logic Circuit

W

W

P

_

PD

P

_

D

D


Integrated circuits ics l.jpg

Integrated Circuits (ICs)

  • Used to implement combinational logic circuits

    • We use the TTL family (transistor transistor logic)


Ic identification l.jpg

1

14

1

1

14

14

2

13

2

2

13

13

3

12

3

3

12

12

4

11

A 1

V cc

4

4

11

11

Y 1

A 6

5

10

5

5

10

10

A 1

V cc

A 2

Y 6

A 1

V cc

B 1

B 4

Y 2

A 5

6

9

B 1

B 4

6

6

9

9

Y 1

A 4

A 3

Y 5

Y 1

A 4

A 2

Y 4

7

8

Y 3

A 2

A 4

Y 4

B 2

7

7

8

8

B 3

B 2

B 3

GND

Y 4

Y 2

A 3

Y 2

A 3

GND

Y 3

GND

Y 3

IC Identification

7404

Inverter Chip

7408

AND Chip

7432

OR Chip


Digital logic trainer l.jpg

IC Chip

IC Chip

Digital Logic Trainer

  • Complete diagram on page 98

  • Breadboard

    • Points with a line through them represent the same connection line


Materials for lab l.jpg

Materials for Lab

  • Digital/Analog Trainer

  • 7432 2-Input OR gate IC

  • 7408 2-Input AND gate IC

  • 7404 Hex Inverter (NOT gate) IC

  • Hook-up Wire

  • Computer equipped with LabVIEW


Problem statement l.jpg

Problem Statement

  • A farmer has two barns

    • A hen is free to move about.

    • A supply of corn is moved periodically from one barn to the other.

    • He wants to protect the hen from a predator fox, and also prevent the hen from eating the supply of corn.

  • An engineering student is hired to design an alarm system, using digital electronics. It will activate under the following conditions:

    • The fox and the hen are in the same barn.

    • The hen and the corn supply are in the same barn.


Problem statement17 l.jpg

Problem Statement

  • Design a combination logic circuit that will accomplish this task.

    • The design should be cost effective, using the least amount of gates and input variables.

  • The logical output of the circuit should be connected to a lamp.

    • The lamp being “on” indicates alarm activation

    • The lamp being “off” indicates alarm deactivation.

  • The fox and hen and corn must be present in either barn 1 or barn 2

    • Presence in barn 1=“1”

    • Presence in barn 2=“0”


Procedure l.jpg

Procedure

  • Truth Table

    • Determine what are the input variables and the output variable

    • Decide how many combinations there should be

    • Create and complete the truth table on a sheet of paper

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Procedure19 l.jpg

Procedure

  • Boolean Expression

    • Gather all the combinations that produced a “1” for the output

    • Create a Boolean expression from these smaller expressions

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Procedure20 l.jpg

Procedure

  • K-Map

    • Create a K-Map table

    • Be sure to only have one variable change states at a time from one box to another

    • Use the Boolean expression to fill in the “1’s”

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Procedure21 l.jpg

Procedure

  • Simplified Boolean Expression

    • Use the K-Map to circle the pairs of 1’s

    • The 1’s may only be circled in multiples of 2, starting from the largest possible combination and working its way down

    • Write down the new simplified expression

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Procedure22 l.jpg

Procedure

  • Logic Circuit Diagram

    • Use the new simplified expression to design a logic circuit

    • Have your instructor check your work

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Procedure23 l.jpg

Procedure

  • Digital Trainer

    • Do NOT plug anything in until your instructor has looked over your work

    • Use the logic circuit and IC chip diagram to create the actual circuit on the breadboard

    • Be sure to connect each of the ICs to Ground and VCC - 5V

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Procedure24 l.jpg

AND

OR

NOT

Procedure

  • LabVIEW Simulation

    • With the use of your logic circuit diagram - recreate the circuit in LabVIEW

    • The front panel should have three control switches representing the variables and one Boolean indicator to represent the output

    • HINT: LabVIEW has the following built in comparison functions:

  • Truth Table

  • Boolean Expression

  • K-Map

  • Simplified Boolean Expression

  • Logic Circuit

  • Digital Trainer

  • LabVIEW Simulation


Written assignment l.jpg

Written Assignment

  • Full Team Report (one report per team)

  • Use the guidelines on page 5 for help

  • Include original data with instructor’s initials

  • Original tables and work should be re-written so it is legible

  • Include a printout of the LabVIEW front and diagram panel

  • Include the topics found on the next slide

  • Remember to create a title page


Written topics l.jpg

Written Topics

  • Each of the following topics must be addressed in the full report and should be placed in the proper sections

    • What are possible applications of digital electronics?

    • Account for any error made during the lab

    • Compare the problem before and after it was simplified

    • What are some advantages of minimization using digital logic?


Recitation topics l.jpg

Recitation Topics

  • If your design did not work the first time, discuss why

  • Discuss how the digital circuit and its design would be affected if barn one had an alarm bell and barn two has an alarm horn


Closing l.jpg

Closing

  • Return all the equipment back to your instructor


  • Login