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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

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

Digital Logic Trainer

Materials for Lab

Problem Statement

Procedure

Written Assignment

Written Topics

Recitation Topics

Closing

Overview


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

  • 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 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

  • 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)


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


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


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?


_ _

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


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)

  • Used to implement combinational logic circuits

    • We use the TTL family (transistor transistor logic)


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


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

  • 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

  • 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 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

  • 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


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


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


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


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


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


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

  • 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

  • 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

  • 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

  • Return all the equipment back to your instructor


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