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Using Digital Logic and Technology in the 21st Century Classroom

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Using Digital Logic and Technology in the21st Century Classroom

Presenters

- Tony White (twhite@neenah.k12.wi.us)
- Technology & Engineering Teacher at Neenah HS
- Lisa O’Neill (loneill@neenah.k12.wi.us)
- Math Teacher at Neenah HS

LogiSim Software Needed - Free

http://ozark.hendrix.edu/~burch/logisim/

DOWNLOAD NOW

Using Digital Logic and Technology in the21st Century Classroom

History

- Neenah HS implemented Project Lead the Way (PLTW) in 2009-10

Cross-Curricular Exposure

- Identify students in ALL curricular areas – Peak students interest in STEM

Year 1

- Trained 2 Technology teachers in Introduction to Engineering Design (IED)

Year 2

- Trained 1 Technology teacher & 2 Science teachers in Principles of Engineering (POE)

Year 3

- Trained 1 Technology teacher & 1 Math teacher in Digital Electronics (DE)

Using Digital Logic and Technology in the21st Century Classroom

Co-Teaching

PLTW Summer Training 2011 – Digital Electronics

- Technology & Math teacher discussed how digital logic would be great to teach to Math classes

Fall 2011

- Advanced Geometry Class – In math classes we teach Logic along with proofs.
- Instead of teaching the old (boring) way of logic wanted to incorporate a more rigorous and relevant way to teach.
- Math & Technology teacher collaborated and co-taught the Advanced Geometry class using the digital logic portion of Digital Electronics to teach logic and proofs.

21st century skills into the classroom

Relate math to real world

Cross-Curricula Teaching

Why use Digital Electronics in Math Courses

It is an exact science

Logic circuits are very unforgiving just like proofs.

To create a version of a modern day proof.

Truth Tables & Logic Expressions

Objective 1

Introduction to Digital Logic (Basics)

This presentation will demonstrate how to…

- What are the 1’s and 0’s in Logic
- Constructing a truth table
- 2 Inputs
- General Problem
- Math Based Problem
- 3 Inputs
- Math Based Problem
- Write a Sum-Of-Products (SOP) logic expression from a truth table
- Given design specifications (i.e., word problem) create a Truth Table and Write SOP logic Expression

End Product

EQUALS

EQUALS

EQUALS

Design

Specifications

Truth Table

Logic

Expression

A. What are the 1’s and 0’s in Logic?

- 1’s and 0’s are the heart and soul of computer language. This is binary. Binary is the number system that computers understand
- Typically in the world of computers, and in the case of TRUTH TABLES

0’s mean off or false

1’s mean on or true

B. Constructing A Truth Table (Example 1)

- A truth table shows how a logic design’s output respond to ALL combinations of possible inputs.
- A logic design with N inputs will have 2N input combinations.

3 Inputs

2 Inputs

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

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1

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1

All possibilities

(This is known for all Truth Tables)

1. Construct a Truth Table-2 Inputs (example #2)

Create a truth table to represent this situation:

I want to pick all girls in the class who have glasses.

The “truth” or how you get “picked” is to be a girl AND to have glasses.

Step 1) How many Inputs?

= 2 (Girls & Glasses)

Step 2) 2N = 22 = 4 Columns

- Output
- Girls with Glasses

- Input 1GIRL

- Input 2
- GLASSES

Step 3) Create Truth Table with 4 Columns

Step 4) Label Input 1 & Input 2

0

0

0

Step 5) Label Output

0

0

1

Step 6) Fill in 0s & 1s --- All possible solutions

0

1

0

Step 7) Fill in Outputs

* This is an “AND” problem

* We only care when

Girl “AND” Glasses are True or “1”

1

1

1

1. Construct a Truth Table-2 Inputs (example #3)

Create a truth table to represent this situation:

“Polygons that are squares”.

The “truth” is” only the polygons that are squares.

Identify the inputs

4 sides?

Sides ≅?

What make a square a square?

0

0

1

1

0

1

0

1

0

0

0

1

Number of sides, sides the same

2) Create the truth table

What row are you concerned with?

Why?

THAT”S where the TRUTH located for this problem! HOW DO YOU know?????

2. Construct a Truth Table-3 Inputs (example #4)

Create a truth table to represent this situation:

“What makes a polygon a Right Isosceles Triangle”.

The “truth” is” only the polygons THAT ARE Right Isosceles Triangles.

#of sides

2 sides ≅ ?

rt. Angle?

rt.isos. Δ?

Identify the inputs

0

0

0

0

1

1

1

1

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1

What make Right Isosceles Triangle?

Number of sides, two sides the same

right angle

Create the truth table-DIFFERENT THIS TIME!

2N = 23 = 8 Columns

What row are you concerned with?

Why?

THAT”S where the TRUTH located for this problem! HOW DO YOU know?????

C. Logic Expression From Truth Table (example #5)

- Write the Minterm adjacent to every row in the truth table that contains a one in the output column.
- WE ARE ONLY CONCERENED WHERE THE OUTPUTS ARE 1.
- Write the Sum-Of-Products (SOP) logic expression by summing together all of the MinTerms.

Ex. X = 1 = 0

- Example
- Write the SOP logic expression for the output F5 in the truth table below.

MinTerms

SOP Logic Expression

Practice #1: T/T→Logic Expression

- Example
- Write the SOP logic expression for the output F6 in the truth table below.

Solution

Answer Key Provided

D. Truth Table from Design Specs (example #6)

- Create a
- Truth Table
- Write MinTerms
- Write SOP
- Write Logic Expression

- Example
- A large fuel tank has sensors that monitor temperature and pressure. Both sensors output 0 if they are within safety range. An alarm will sound if either sensor indicates an unsafe condition is present. Create a truth table for this logic design.

- Assignment :
- P: Pressure Sensor → 0=Safe / 1=Unsafe
- T: Temperature Sensor → 0=Safe / 1=Unsafe
- A: Alarm → 0=Alarm Off / 1=Alarm On

D. Truth Table from Design Specs - ANSWER

- Example
- A large fuel tank has sensors that monitor temperature and pressure. Both sensors output a logic LOW if they are within safety range. An alarm will sound if either sensor indicates an unsafe condition is present. Create a truth table for this logic design.

1. Truth Table

- Assignment :
- P: Pressure Sensor → 0=Safe / 1=Unsafe
- T: Temperature Sensor → 0=Safe / 1=Unsafe
- A: Alarm → 0=Alarm Off / 1=Alarm On

2. MinTerms

0

1

1

1

3. Logic Expression

Introduction to LogiSim software

Objective 2

This presentation will demonstrate how to…

- Constructing a truth table – 3 Inputs
- Write a Sum-Of-Products (SOP) logic expression from a truth table
- Create a truth table from a set of design specifications (i.e., word problem)
- Design Class Problem on LogiSim

Switch = Pin Inverter AND Gate OR Gate LED

Example #7Try on own before next slide

- Your teacher keeps her final exams in her office. For security reasons, she would like you to design an alarm system for her office. The office has a window and door that are equipped with sensors that output a one when they are secured (i.e., closed). When the alarm system is turned on with a key, the siren should sound if either the window or door is unsecured (i.e., opened).

MinTerms

Assignment Name____________________________

Truth Table _____ 5

Write MinTerms _____ 5

Write Logic Expression _____ 5

- K : Key → 0=System Off / 1=System On
- D : Door Sensor → 0=Open / 1=Closed
- W : Window Sensor → 0=Open / 1=Closed
- S : Siren → 1=On / 0=Off

Logic ExpressionSiren = ____________________________

Class Example ANSWER

- Your teacher keeps her final exams in her office. For security reasons, she would like you to design an alarm system for her office. The office has a window and door that are equipped with sensors that output a one when they are secured (i.e., closed). When the alarm system is turned on with a key, the siren should sound if either the window or door is unsecured (i.e., opened).

MinTerms

Assignment Name____________________________

Truth Table _____ 5

Write MinTerms _____ 5

Write Logic Expression _____ 5

0

0

0

0

1

1

1

0

- K : Key → 0=System Off / 1=System On
- D : Door Sensor → 0=Open / 1=Closed
- W : Window Sensor → 0=Open / 1=Closed
- S : Siren → 1=On / 0=Off

Logic ExpressionSiren = ____________________________

Download LogiSim

http://ozark.hendrix.edu/~burch/logisim/

Introduction to LogiSim

Step 1) How many Inputs --- How many Pins Needed

Step 2) Need 2 Inverters --- K is always ON

Step 3) Need 3 AND Gates --- One for each Input

Step 4) Need 3 OR Gates --- One for each Input

Step 5) Need 1 LED --- Under Input/Output

Layout Example

Need to add wires

* Before Inverter means On/True/1

* After Inverter means Off/False/0

Step 5) What makes each AND Gate True

Top AND Gate = KD’W’

Middle AND Gate = KD’W

Bottom AND Gate = KDW’

ADD Wires for Top AND Gate = KD’W’

ADD Wires for Top AND Gate = KD’W

ADD Wires for Top AND Gate = KDW’

Construct a Truth Table-3 InputsClass Problem – Do on own

Polygons that have 4 sides the same OR opposite sides parallel AND 4 right angles

Assignment

Construct Truth Table

Fill in Inputs

Fill in Possible Solutions in Truth Table

Fill in 1’s when Output is TRUE

Write MinTerms for True Outputs

Write SOP Expression

Design on LogiSim

MinTerms

Logic ExpressionPolygons = ____________________________

Answer Key Provided

Practice #1: T/T→Logic ExpressionANSWER KEY

- Example
- Write the SOP logic expression for the output F6 in the truth table below.

Solution

Answer from Slide 13

Construct a Truth Table-3 Inputs - ANSWER

Polygons that have 4 sides the same OR opposite sides parallel AND 4 right angles

4 sides ≅

Polygons

opp sides ll

4 rt angles.

MinTerms

0

1

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1

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Assignment

Construct Truth Table

Fill in Inputs

Fill in Possible Solutions in Truth Table

Fill in 1’s when Output is TRUE

Write MinTerms for True Outputs

Write SOP Expression

Design on LogiSim

Logic ExpressionPolygons = ____________________________

Answer from Slide 29

Quadrilateral MachineLesson Plan

Providing a Differentiated Lesson plan for a Quadrilateral Machine

* Use Lesson plan as a template to modify to your class needs

* The Lesson plan is not perfect (New) – but students learn the concepts (Taught to students at NHS)

* This is an new process and constantly evolving

* We will send updates to those who provide an email

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