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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

LABORATORY11:Digital Logic Circuits

General Engineering

Polytechnic University

overview
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
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
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
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
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
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
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
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
_ _

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
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
Integrated Circuits (ICs)
  • Used to implement combinational logic circuits
    • We use the TTL family (transistor transistor logic)
ic identification
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

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
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
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
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
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
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
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
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
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
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
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
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
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
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
Closing
  • Return all the equipment back to your instructor
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