Digital Logic Circuits and Design Principles

EG1003: Introduction to Engineering and Design
Digital Logic Circuits
Digital Logic Circuits
Overview
Objective
Background
Materials
Procedure
Report / Presentation
Closing
Objective
Understand logic gates and digital logic circuits
Design combinational logic circuit
Activate under specific conditions
Test with LabVIEW
Test using NI-ELVIS prototyping board
Logic Functions
AND - “All or nothing operator”
Output high (1) only when ALL inputs are high (1)
OR gate - “Any or all operator”
Output high (1) when at least ONE input is high
(1)
NOT operator – “Inverter”
Output always opposite of input
Only one input and one output
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Sample Problem
ATM machine has three options:
Print statement
Withdraw money
Deposit money
ATM machine will charge $1.00 to:
Withdraw
Print out statement with no transactions
No charge for:
Deposits without withdrawal
Competition Rules
A truth table displays all
possible input / output
combinations.
INPUT
 
  OUTPUT
P = Print
 
  C = Charge
W = Withdraw
D = Deposit
0 = “do not”
 
  0 = $0.00
1 = “do”
 
        1 = $1.00
 
 
C
 
=
 
 
 
 
 
 
P
W
D
 
 
   + PWD
 
  
+ PWD
 
  
+ PWD
 
  
+ PWD
Outputs with a value
Outputs with a value
of “ONE” are kept
of “ONE” are kept
Boolean Equations
 
W
W
C
 
=
 
P
W
D
+
 
P
W
D
+
 
P
W
D
 
+
 
P
W
D
 
+
 
P
W
D
 
P
P
 
P
P
 
P
P
 
P
P
 
W
W
 
W
W
 
W
W
 
D
D
 
D
D
 
1
1
 
1
1
 
1
1
 
1
1
 
1
1
 
                                                   _
Why can’t you switch PW and PW?
 
0
0
 
1
1
 
Why can’t you loop the three
adjacent 1s in the top row together?
 
P
P
W
W
D
D
 
P
P
W
W
D
D
 
P
P
W
W
D
D
 
0
0
 
0
0
 
1
1
 
1
1
 
1
1
 
1
1
 
0
0
 
0
0
 
0
0
 
0
0
 
0
0
Karnaugh Maps (K-maps)
Karnaugh Maps (K-maps)
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P
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D
+
 
P
W
D
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P
W
D
 
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P
W
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+
 
P
W
D
 
C
 
=
 
   W
Opposite
values
cancel out
 
     
  
_
+ PD
0
0
0
0
0
0
Simplified Boolean Equation
 
 
 
 
 
 
 
 
 
 
 
 
_
_
P
P
W
W
D
D
C
 
=
 
W
 
+
 
P
D
Opposite values in circles cancel out
Opposite values in circles cancel out
Simplified Boolean Equation
 
W
W
 
P
 
D
 
_
D
 
 
 
 
 
 
 
 
 
_
_
P
P
D
D
 
W
W
 
P
Combinational Logic Circuit
Integrated Circuits (ICs)
Used for implementation of combinational logic
circuits
Use TTL family (transistor transistor logic)
IC Identification
IC Identification
Materials for Lab
Materials for Lab
Computer equipped with LabVIEW
NI-ELVIS II+ Prototyping Board
DIP Switch
Hook-up Wire
Problem Statement
Problem Statement
A farmer has 2 barns
3 items: fox, hen, corn
Items can be in any barn, in any combination
Concerns:
Protect hen from fox
Protect corn from hen
Design alarm system using digital electronics.  Alarm
sounds when:
Fox and hen are in same barn
Hen and corn are in same barn
Problem Statement
Problem Statement
Design combination logic circuit for alarm system:
Use least amount of gates and input variables
(cost effectiveness)
Logical circuit output connected to LED
LED “on” indicates alarm activation
LED “off” indicates no problem (alarm off)
Fox, hen and corn must be in barn 1 or barn 2
Presence in barn 1 = 1
Presence in barn 2 = 0
Procedure
Procedure
Truth Table
Determine input and output
variable (s)
How many combinations are
there?
Complete truth table on a sheet
of paper
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Procedure
Procedure
Boolean Expression
Gather all combinations that
produce a 1 for output
Create a Boolean expression
from these smaller expressions
(independent conditions)
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Procedure
Procedure
K-Map
Create a K-Map table
Only have one variable change
state at a time between
adjacent boxes
Use the Boolean expression to
fill in the 1’s
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Procedure
Procedure
Simplified Boolean Expression
Use K-Map to circle groups of
1’s
1’s may only be circled in
powers of 2, starting from
largest possible combination
and working downward
Write new simplified expression
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Procedure
Procedure
Logic Circuit Diagram
Use new simplified Boolean
expression to design a logic
circuit
Have TA check/initial work
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Procedure
Procedure
LabVIEW Simulation
Create logic circuit in LabVIEW based
on theoretical work
Front panel
3 control switches represent input
variables
1 Boolean indicator shows output
HINT:  some LabVIEW comparison functions are:
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Procedure
Procedure
NI-ELVIS Prototyping Board
Do NOT electrically connect anything until TA
has reviewed your work
Connect +5V and ground to the DIP switch
Use created logic circuit and IC chip diagram to
wire actual circuit on the prototyping board
Be sure to connect each of the ICs to “Ground”
and “+5V” (circuit power)
Connect final output to an LED.
**VCC is an acronym:
**Voltage at the Common Collector (+5V)
Truth Table
Boolean Expression
K-Map
Simplified Boolean
Expression
Logic Circuit
LabVIEW Simulation
NI-ELVIS
Assignment: Report
Assignment: Report
Individual Report
Title page
Discussion topics in the manual
Scan in data and lab notes
Original tables and work should be legible
Include screenshots of LabVIEW front and back
panels
Assignment: Presentation
Assignment: Presentation
Team presentation
Professional-looking tables
Include screen shots of your programs
Photo of functioning LED assembly
Explain steps taken to complete lab
Be prepared to provide walk-through
Include lab data
Refer to “Creating PowerPoint Presentations”
found in Online Manual
Closing
Closing
Have all original data signed by TA
Each team member should have turn using
software
Submit all work electronically
Return all unused materials to TA
Slide Note
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Explore the world of digital logic circuits with a focus on logic gates, truth tables, boolean equations, and Karnaugh maps. Learn how to design combinational logic circuits, analyze different logic functions, and solve sample problems related to digital logic. Get hands-on experience with LabVIEW and the NI-ELVIS prototyping board to test and validate your designs.


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  1. EG1003: Introduction to Engineering and Design Digital Logic Circuits Image:lab_logic_1.jpg Image:lab_logic_4.jpg Image:lab_logic_7.jpg

  2. Overview Objective Background Materials Procedure Report / Presentation Closing

  3. Objective Understand logic gates and digital logic circuits Design combinational logic circuit Activate under specific conditions Test with LabVIEW Test using NI-ELVIS prototyping board

  4. Logic Functions AND - All or nothing operator Output high (1) only when ALL inputs are high (1) OR gate - Any or all operator Output high (1) when at least ONE input is high (1) NOT operator Inverter Output always opposite of input Only one input and one output

  5. Logic Functions Truth Table Inputs A B Boolean Expression Output Y Logic Function Logic Symbol 0 0 0 0 1 0 AND A B = Y 1 0 0 1 1 1 0 0 0 0 1 1 OR A + B = Y 1 0 1 1 1 1 0 - 1 A = NOT 1 - 0

  6. Sample Problem ATM machine has three options: Print statement Withdraw money Deposit money ATM machine will charge $1.00 to: Withdraw Print out statement with no transactions No charge for: Deposits without withdrawal

  7. Competition Rules A truth table displays all possible input / output combinations. INPUTS W 0 0 1 1 OUTPUT C 0 0 1 1 1 0 1 D 0 P 0 0 0 0 1 1 0 1 INPUT OUTPUT P = Print W = Withdraw D = Deposit C = Charge 0 0 1 0 1 1 1 0 1 0 = do not 1 = do 0 = $0.00 1 = $1.00 1 1 1

  8. Boolean Equations Outputs with a value of ONE are kept INPUTS W 0 0 1 1 OUTPUT C 0 0 1 1 1 0 1 D 0 P 0 0 0 0 1 C = PWD 1 0 1 + PWD + PWD + PWD + PWD 0 0 1 0 1 1 1 0 1 1 1 1

  9. Karnaugh Maps (K-maps) C = PWD+ PWD+ PWD + PWD + PWD PWD PWD PWD 0 1 0 0 1 1 1 0 P W P W 1 P W P W 1 0 1 1 0 1 D D 0 0 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 0 0 0 1 1 1 1 0 P W P W 1 P W P W 1 0 1 1 0 1 D D 0 0 1 NOTE:Circle neighboring ONES in powers of 2. Try to find the greatest amount of neighbors. Only overlap circles as a last resort!

  11. Simplified Boolean Equation _ _ PWD _ PWD D D 0 0 Opposite values cancel out P P P W W W W 1 1 _ 1 1 _ _ _ 1 1 1 1 1 1 W C = + PD PWD _ 1 0 P PWD PWD PWD

  12. Simplified Boolean Equation Opposite values in circles cancel out _ _ PWD PWD Step 1 D D 0 0 3 _ PWD _ P P P W W W W _ = W 2 PWD PWD 4 1 1 1 1 _ _ 1 0 Step 1 PWD _ _ PWD = PD P C = W + PD

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

  14. Integrated Circuits (ICs) Used for implementation of combinational logic circuits Use TTL family (transistor transistor logic)

  15. IC Identification

  16. Materials for Lab Computer equipped with LabVIEW NI-ELVIS II+ Prototyping Board DIP Switch Hook-up Wire

  17. Problem Statement A farmer has 2 barns 3 items: fox, hen, corn Items can be in any barn, in any combination Concerns: Protect hen from fox Protect corn from hen Design alarm system using digital electronics. Alarm sounds when: Fox and hen are in same barn Hen and corn are in same barn

  18. Problem Statement Design combination logic circuit for alarm system: Use least amount of gates and input variables (cost effectiveness) Logical circuit output connected to LED LED on indicates alarm activation LED off indicates no problem (alarm off) Fox, hen and corn must be in barn 1 or barn 2 Presence in barn 1 = 1 Presence in barn 2 = 0

  19. Procedure Truth Table Determine input and output variable (s) How many combinations are there? Complete truth table on a sheet of paper Truth Table Boolean Expression K-Map Simplified Boolean Expression Logic Circuit LabVIEW Simulation NI-ELVIS

  20. Procedure Boolean Expression Gather all combinations that produce a 1 for output Truth Table Boolean Expression K-Map Simplified Boolean Expression Create a Boolean expression from these smaller expressions (independent conditions) Logic Circuit LabVIEW Simulation NI-ELVIS

  21. Procedure K-Map Create a K-Map table Only have one variable change state at a time between adjacent boxes Use the Boolean expression to fill in the 1 s Truth Table Boolean Expression K-Map Simplified Boolean Expression Logic Circuit LabVIEW Simulation NI-ELVIS

  22. Procedure Simplified Boolean Expression Use K-Map to circle groups of 1 s 1 s may only be circled in powers of 2, starting from largest possible combination and working downward Write new simplified expression Truth Table Boolean Expression K-Map Simplified Boolean Expression Logic Circuit LabVIEW Simulation NI-ELVIS

  23. Procedure Logic Circuit Diagram Use new simplified Boolean expression to design a logic circuit Truth Table Boolean Expression K-Map Simplified Boolean Expression Logic Circuit Have TA check/initial work LabVIEW Simulation NI-ELVIS

  24. Procedure LabVIEW Simulation Create logic circuit in LabVIEW based on theoretical work Front panel 3 control switches represent input variables 1 Boolean indicator shows output Truth Table Boolean Expression K-Map Simplified Boolean Expression Logic Circuit LabVIEW Simulation HINT: some LabVIEW comparison functions are: NI-ELVIS OR NOT AND

  25. Procedure NI-ELVIS Prototyping Board Do NOT electrically connect anything until TA has reviewed your work Connect +5V and ground to the DIP switch Use created logic circuit and IC chip diagram to wire actual circuit on the prototyping board Be sure to connect each of the ICs to Ground and +5V (circuit power) Connect final output to an LED. **VCC is an acronym: **Voltage at the Common Collector (+5V) Truth Table Boolean Expression K-Map Simplified Boolean Expression Logic Circuit LabVIEW Simulation NI-ELVIS

  26. Assignment: Report Individual Report Title page Discussion topics in the manual Scan in data and lab notes Original tables and work should be legible Include screenshots of LabVIEW front and back panels

  27. Assignment: Presentation Team presentation Professional-looking tables Include screen shots of your programs Photo of functioning LED assembly Explain steps taken to complete lab Be prepared to provide walk-through Include lab data Refer to Creating PowerPoint Presentations found in Online Manual

  28. Closing Have all original data signed by TA Each team member should have turn using software Submit all work electronically Return all unused materials to TA

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