1. Using Digital Logic and Technology in the 21st 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 1

2. Using Digital Logic and Technology in the 21st Century Classroom History o Neenah HS implemented Project Lead the Way (PLTW) in 2009-10 Cross-Curricular Exposure o Identify students in ALL curricular areas – Peak students interest in STEM Year 1 o Trained 2 Technology teachers in Introduction to Engineering Design (IED) Year 2 o Trained 1 Technology teacher & 2 Science teachers in Principles of Engineering (POE) Year 3 o Trained 1 Technology teacher & 1 Math teacher in Digital Electronics (DE) 2

3. Using Digital Logic and Technology in the 21st Century Classroom Co-Teaching PLTW Summer Training 2011 – Digital Electronics o Technology & Math teacher discussed how digital logic would be great to teach to Math classes Fall 2011 o Advanced Geometry Class – In math classes we teach Logic along with proofs. o Instead of teaching the old (boring) way of logic wanted to incorporate a more rigorous and relevant way to teach. o Math & Technology teacher collaborated and co-taught the Advanced Geometry class using the digital logic portion of Digital Electronics to teach logic and proofs. 3

4. Relate math to real world To create a version of a modern day proof. It is an exact science Rigorous, Relevant, 21 st century skills into the classroom Logic circuits are very unforgiving just like proofs. Why use Digital Electronics in Math Courses Cross-Curricula Teaching 4

5. Truth Tables & Logic Expressions Advanced Geometry and Digital Electronics Proof Machine Project 5

6. Truth Tables & Logic Expressions Objective 1 Introduction to Digital Logic (Basics) This presentation will demonstrate how to… A.What are the 1’s and 0’s in Logic B.Constructing a truth table 1.2 Inputs  General Problem  Math Based Problem 2.3 Inputs  Math Based Problem C.Write a Sum-Of-Products (SOP) logic expression from a truth table D.Given design specifications (i.e., word problem) create a Truth Table and Write SOP logic Expression XYOUT 000 010 101 110 EQUALS Design Specifications Truth Table Logic Expression EQUALS End Product 6

7. 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’smean off or false 1’smean on or true 7

8. 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 2 N input combinations. Input 1Input 2Output 2 Inputs Input 1Input 2Input 3Output 3 Inputs 0 0 0 1 0 1 0 1 0 0 1 1 0000111100001111 0011001100110011 0101010101010101 0110001101100011 All possibilities (This is known for all Truth Tables) 8

9. 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. 0 0 0 1 Step 1) How many Inputs? = 2 (Girls & Glasses) Step 2) 2 N = 2 2 = 4 Columns Step 3) Create Truth Table with 4 Columns Input 1 GIRL Input 2 GLASSES Output Girls with Glasses Step 4) Label Input 1 & Input 2 Step 5) Label Output Step 6) Fill in 0s & 1s --- All possible solutions 00 01 10 11 Step 7) Fill in Outputs * This is an “AND” problem * We only care when Girl “AND” Glasses are True or “1” 9

10. 1. Construct a Truth Table-2 Inputs (example #3) SQUARE? Number of sides, sides the same What row are you concerned with? Why? Create a truth table to represent this situation: “Polygons that are squares”. The “truth” is” only the polygons that are squares. 1)Identify the inputs 2) Create the truth table What make a square a square? THAT”S where the TRUTH located for this problem! HOW DO YOU know????? 4 sides? Sides ≅ ? 00110011 01010101 00010001 10

11. 2. Construct a Truth Table-3 Inputs (example #4) Number of sides, two sides the same right angle What row are you concerned with? Why? 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. 1)Identify the inputs 2)Create the truth table- DIFFERENT THIS TIME! 2 N = 2 3 = 8 Columns What make Right Isosceles Triangle? THAT”S where the TRUTH located for this problem! HOW DO YOU know????? #of sides 2 sides ≅ ? rt. Angle?rt.isos. Δ? 0101010101010101 0011001100110011 0000111100001111 0000000100000001

12. 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. Example Write the SOP logic expression for the output F 5 in the truth table below. XYZF5F5 0000 0011 0100 0111 1001 1010 1101 1110 MinTermsSOP Logic Expression Ex. X = 1 = 0 12

13. Practice #1: T/T→Logic Expression Example Write the SOP logic expression for the output F 6 in the truth table below. ABCDF6F6 00000 00011 00100 00111 01000 01010 01100 01110 10000 10010 10100 10111 11000 11011 11100 11111 Solution Answer Key Provided 13

14. D. Truth Table from Design Specs (example #6) Create a 1)Truth Table 2)Write MinTerms 3)Write SOP 4)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 14

15. 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. PTA 00 01 10 11 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 3. Logic Expression 1. Truth Table 0 1 1 1 D. Truth Table from Design Specs - ANSWER 15

16. Introduction to LogiSim software Objective 2 This presentation will demonstrate how to… A.Constructing a truth table – 3 Inputs B.Write a Sum-Of-Products (SOP) logic expression from a truth table C.Create a truth table from a set of design specifications (i.e., word problem) D.Design Class Problem on LogiSim Switch = PinInverterAND GateOR GateLED 16

17. Example #7 Try 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). AssignmentName____________________________ Truth Table_____ 5 Write MinTerms_____ 5 Write Logic Expression _____ 5 KDWS 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 Expression Siren = ____________________________ MinTerms 17

18. 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). AssignmentName____________________________ 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 Expression Siren = ____________________________ KDWS 000 001 010 011 100 101 110 111 MinTerms 0000111000001110 18

19. Download LogiSim http://ozark.hendrix.edu/~burch/logisim/ 19

20. Introduction to LogiSim Step 1) How many Inputs --- How many Pins Needed Step 2) Need 2 Inverters --- K is always ON Step 4) Need 3 OR Gates --- One for each Input Step 3) Need 3 AND Gates --- One for each Input Layout Example Step 5) Need 1 LED --- Under Input/Output 20

21. Introduction to LogiSim Need to add wires Step 5) What makes each AND Gate True Top AND Gate = KD’W’ Middle AND Gate= KD’W Bottom AND Gate= KDW’ * Before Inverter means On/True/1 * After Inverter means Off/False/0 21

22. Introduction to LogiSim ADD Wires for Top AND Gate = KD’W’ 22

23. Introduction to LogiSim ADD Wires for Top AND Gate = KD’W 23

24. Introduction to LogiSim ADD Wires for Top AND Gate = KDW’ 24

25. Introduction to LogiSim Add wires from AND Gates to OR Gates Add wire from OR Gate to LED 25

26. Example #7 on LogiSim 26

27. Example #7 on Multisim 27

28. Construct a Truth Table-3 Inputs Class Problem – Do on own Polygons that have 4 sides the same OR opposite sides parallel AND 4 right angles Logic Expression Polygons = ____________________________ Assignment 1.Construct Truth Table 2.Fill in Inputs 3.Fill in Possible Solutions in Truth Table 4.Fill in 1’s when Output is TRUE 5.Write MinTerms for True Outputs 6.Write SOP Expression 7.Design on LogiSim MinTerms Answer Key Provided 28

29. Questions? 29

30. Answer Key 30

31. Practice #1: T/T→Logic Expression ANSWER KEY Example Write the SOP logic expression for the output F 6 in the truth table below. ABCDF6F6 00000 00011 00100 00111 01000 01010 01100 01110 10000 10010 10100 10111 11000 11011 11100 11111 Solution Answer from Slide 13 31

32. Construct a Truth Table-3 Inputs - ANSWER Polygons that have 4 sides the same OR opposite sides parallel AND 4 right angles 4 sides ≅ opp sides ll 4 rt angles. Polygons 0000111100001111 0011001100110011 0101010101010101 0001010100010101 Logic Expression Polygons = ____________________________ Assignment 1.Construct Truth Table 2.Fill in Inputs 3.Fill in Possible Solutions in Truth Table 4.Fill in 1’s when Output is TRUE 5.Write MinTerms for True Outputs 6.Write SOP Expression 7.Design on LogiSim MinTerms Answer from Slide 29 32

33. Practice #2 -- Answer 33

34. Quadrilateral Machine Lesson Plan * 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 Providing a Differentiated Lesson plan for a Quadrilateral Machine 34