1. LABORATORY11: Digital Logic Circuits
General Engineering
Polytechnic University

2. 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

3. 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

4. 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

5. Logic Functions AND OR NOT Logic Function Logic Symbol BooleanĀ B Y
A • B = Y
A + B = Y
A = Ā
AND OR
NOT
Logic Function
Logic Symbol
Boolean
Expression
Truth Table
Inputs Outputs 1

6. 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)

7. Truth Table INPUTS OUTPUT P W D C 1 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 P W D C 1

8. Boolean Equation = PWD C = + PWD + PWD + PWD + PWD INPUTS OUTPUT P W D
Outputs with a value of “ONE” are kept
INPUTS
OUTPUT P W D C 1
= PWD
C =
+ PWD
+ PWD
+ PWD
+ PWD

9. 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 1 1 1 1 P W P W P W P W D 1 1 1 1 D 1 1 _
Why can’t you switch PW and PW?
Why can’t you loop the three
adjacent 1s in the top row together?

10. Karnaugh Maps (K-maps)
C = PWD+ PWD+ PWD + PWD + PWD W P D 1
NOTE:Circle neighboring ONES in multiples of 2. Try to find the greatest amount of “neighbors.” Only overlap circles as a last resort

11. Simplified Boolean Equation1
_ _
PWD _
Opposite values cancel out P W D 1 W
C = 1 _
PWD
_ _ _
+ PD

12. Simplified Boolean Equation
Opposite values in circles cancel out P W D
_ _
PWD _
= W 3
Step 1 2 4 1 _
PWD
_ _
= PD
Step 1
C = W + PD

13. Combinational Logic CircuitW
C = W P D + W P D + W P D + W P _ PD P D + P D _ D D

14. Integrated Circuits (ICs)
Used to implement combinational logic circuits
We use the TTL family (transistor transistor logic)

15. IC Identification Y 6 Y 5 Y 4 Y 3 Y 2 Y 1 A 6 A 5 A 4 A 3 A 2 A 1 V cc14 2 4 5 6 7 3 8 9 10 11 12 13
Y 6
Y 5
Y 4
Y 3
Y 2
Y 1
A 6
A 5
A 4
A 3
A 2
A 1
V cc
GND
B 1
B 2
A 4
A 3
A 2
A 1
B 3
B 4
Y 4
Y 3
Y 2
Y 1
V cc
GND 1 14 2 4 5 6 7 3 8 9 10 11 12 13
7404
Inverter Chip
7408
AND Chip
7432
OR Chip 1 14 2 4 5 6 7 3 8 9 10 11 12 13
A 4
A 3
A 2
A 1
Y 4
Y 3
Y 2
Y 1
V cc
GND
B 4
B 3
B 2
B 1

16. Digital Logic Trainer Complete diagram on page 98 Breadboard
Points with a line through them represent the same connection line
IC Chip 

17. Materials for Lab Digital/Analog Trainer 7432 2-Input OR gate IC
Input AND gate IC
7404 Hex Inverter (NOT gate) IC
Hook-up Wire
Computer equipped with LabVIEW

18. 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.

19. 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”

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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
NOT
AND OR

27. 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
What are possible applications of digital electronics?
Account for any errors made during the lab.
Compare the problem before and after it was simplified.
What are some advantages of minimization using digital logic?
How would the digital circuit and its design be affected if barn one had an bell and barn two had an alarm horn?
Explain how the Boolean equation is found using the truth table.
State rules that one must follow when labeling K-maps and grouping the 1’s. From the K-map, how is the simplified Boolean equation found?

28. 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?
What are possible applications of digital electronics?
Account for any errors made during the lab.
Compare the problem before and after it was simplified.
What are some advantages of minimization using digital logic?
How would the digital circuit and its design be affected if barn one had an bell and barn two had an alarm horn?
Explain how the Boolean equation is found using the truth table.
State rules that one must follow when labeling K-maps and grouping the 1’s. From the K-map, how is the simplified Boolean equation found?

29. 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

30. Closing
Return all the equipment back to your instructor