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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

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

### 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

### 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

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

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

7404

Inverter Chip

7408

AND Chip

7432

OR Chip

IC Chip

IC Chip

### Digital Logic Trainer

• Complete diagram on page 98

• 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