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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

- 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

- 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

- 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

= 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

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

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

- 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

- Complete diagram on page 98
- Breadboard
- Points with a line through them represent the same connection line

- 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

- 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.

- 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”

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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?

- 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

- Return all the equipment back to your instructor