The following lectures and exercises should be implemented in the given order, to help build the foundation for understand digital electronics.

Session1: How Processors Compile and Execute Programs
(See PowerPoint Presentation "Survey of Program Compilation and Execution.")

Prerequisites: Students should already know how to program. They can compile and execute programs, preferably in C++.

Duration: 1 Day

Introduction:

It is amazing how you can press the power button on a computer and once it boots up you can do all sorts of cool stuff. However, when you open up the computer you really can’t tell how it all works. This module will attempt to reveal some of the mysteries of the inner workings of a computer. Since this module is geared towards a computer science class, a program in C++ will be compiled and the resulting opcode instructions will be examined.

(This module is intended to be used as an introduction to digital electronics. The Number Systems, Basics of Electronics Circuit, Introduction to Digital Logic, and The Ultimate 2-Bit Binary Adder Circuit module can be used in conjunction with this module to explain digital electronics.)

Objectives:
Students gain an intuition into how computers compile and execute programs.

Associated Maine Learning Results

Mathematics
A. NUMBERS AND NUMBER SENSE
B. COMPUTATION

Science and Technology
J. INQUIRY AND PROBLEM SOLVING
K. SCIENTIFIC REASONING

Required Equipment:

• Laptop or computer
• Visual Studio 6. 0 or above
• Overhead projector for laptop or computer

Procedure

1. The PowerPoint presentation will familiarize students with the main components of a computer such as the memory and the processor.
2. The slides will then describe how the source code the students write will be translated into a form that the processor can understand. The program Prog1Demo.cpp associated with this session should be executed in Visual Studio in the debugging mode on the projector so that the students can see the program execute.
   
   1. Set a breakpoint anywhere in the program.
   2. Select the “Build” menu, Select “Start Debug” option and then click on “Go.”
   3. The program will begin to execute. The program will stop a the breakpoint selected.
   4. Go to the “View” menu, select “Debug Windows”, and click on “Disassembly.”
   5. The source code plus the assembly code is shown in the source window.
   6. Describe to the students how each line of code is translated to the assembly code.
   7. Show how the registers are being used by the program.
   8. You can open up the Intel document “25366618_InstrSet” that describes the instruction set of the Pentium 4 processor and you can explain how the assembly instructions map to the hexadecimal number opcode values.
3. The slides then compare the pros and cons of programming in a high level language like C++ and assembly.
4. Give the quiz.
5. Go over the quiz.

Session 2: Number Systems
(See PowerPoint Presentation "Number Systems.")

Prerequisites: None

Duration: 2-3 Days

Introduction:

This module will give students an intuition of how number systems work. The students will see how something that they take for granted took centuries to evolve and refine. The highly efficient counting methods in use today were not available to people of bygone ages. Many of the mathematical concepts developed in the last millennium would not have been possible without the number system in use today. An efficient number system such as the one in use today allows ideas to progress beyond the numbers themselves. This can be seen how the wieldy and cumbersome number systems developed by people throughout history was an impediment to their mathematical progress. A number system must be transparent otherwise it will lead to a stagnation of mathematical thought.

Objectives:

Students will learn how the present number system functions and the beauty in its efficiency and simplicity.

Associated Maine Learning Results

Mathematics
A. NUMBERS AND NUMBER SENSE
B. COMPUTATION

Science and Technology
J. INQUIRY AND PROBLEM SOLVING
K. SCIENTIFIC REASONING

Required Equipment:

• Laptop or computer
• Overhead projector for laptop or computer
• PowerPoint Presentation: "Number Systems"

Procedure:

1. This session will begin with discussing how the number system has evolved in human history. It discusses the different number systems used by different civilizations.
2. The slides then describe the base 10 number system.
3. The slides then describe the base 8 number system.
4. The slides present the base 16 number system.
5. The slides then present base 2—binary system.
   (It is important to follow this progression because it allows students time to adjust their thinking. Also be sure to distribute the file Base_Chart and the Conversion_Notes among the students. This will help them to see how the different numbering systems compare.)
6. The slides then discuss methods for converting numbers between bases. There are two methods to be used, depending upon whether the base that you are moving to is a larger or smaller base system than the base you are moving from.
7. Show the students the file “People” for comic relief. See how many students get the joke.
8. Give the students the quiz.
9. Discuss the quiz.

Note: It is important to go through this material slowly and to be patient with the students. It can easily take 2-3 days before students fully grasp the concept of number systems. It is important to work out examples on the overhead projector at every step of the way. Call on a student and have them “assist” you as you work out the conversions or enumerate the base numerals.

Session 3: Experiment - Basics of Electronics Circuits
(See PowerPoint presentation "Electronics Theory.")

Prerequisites: Basic Chemistry

Duration: 3-4 Days

Introduction:

This module will expose students to the theory and applications of electronics. This module can be used in conjunction with the GK-12 Sensors! Breadboarding Lab by Erik McCarthy. Erik’s module provides more circuit building exercises. This module contains a PowerPoint presentation that can be used to fully explain the theory behind electronics. However, it should be noted that this module is geared toward preparing students for building digital circuits. As a result, only series circuits are discussed here. Erik’s module is more focused on circuit theory and as a result discusses a wider range of circuit topics such as parallel circuits and equivalent resistance.

Objectives:

1. Students grasp the electronics theory that gives rise to electronics.
2. Students understand the concepts of Current, Voltage, and Resistance.
3. Students use breadboards to build circuits.

Associated Maine Learning Results:

Mathematics

B. COMPUTATION
1) Use various techniques to approximate solutions, determine the reasonableness of answers, and justify the results.
F. MEASUREMENT
1) Use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools.
H. ALGEBRA CONCEPTS
3) Formulate and solve equations and inequalities.
4) Analyze and explain situations using symbolic representations.

Science and Technology

E. STRUCTURE OF MATTER
1) Trace the development of models of the atom to the present and describe how each model reflects the scientific understanding of their time.
5) Describe how atoms are joined by chemical bonding.
6) Compare the physical and chemical characteristics of elements.
H. ENERGY
7) Use mathematics to describe and predict electrical and magnetic activity (e.g., current, resistance, voltage).
8) Compare and contrast how conductors, semiconductors, and superconductors work and describe their present and potential uses.
J. INQUIRY AND PROBLEM SOLVING
1) Make accurate observations using appropriate tools and units of measure.
2) Verify, evaluate, and use results in a purposeful way. This includes analyzing and interpreting data, making predictions based on observed patterns, testing solutions against the original problem conditions, and formulating additional questions.
6) Discover relationships and patterns.
K. SCIENTIFIC REASONING
3) Develop generalizations based on observations.

Required Equipment:

• Laptop or computer
• Overhead projector for laptop or computer
• Breadboards
• Batteries/Power supplies for breadboards
• LEDs
• Heavy gauge wire for breadboards
• Multi-meters

Procedure:

Days 1-2

1. Present the PowerPoint slides associated with this module. (The slides contain lots of information; draw pictures to help describe what is going on.)
2. Ask students questions, some may already know enough to be able to describe some of these concepts.
3. Talk about safe use of electricity.
   
   1. Dangers of taking electrical appliances into showers, bath-tubs, swimming pools.
   2. Discuss how electrical current passing through the body may impede the electrical signal controlling the heart and lead to cardiac arrest.
   3. Discuss how current passing through muscle tissue causes the muscle to “flex/clench.” Tell students that during an electrical shock where a person has “grabbed” on to an “electrically–live” object, he will not be able to release the object.
   4. Tell the students not to build anything that requires power from the wall socket until they know how to do so properly.
   5. Discuss safe use of batteries, i.e. do not plug them in backward, they can explode.
   6. Discuss safe use of transformers during the lab, i.e. do not place the connector in one’s mouth, avoid touching the connector to wet skin, and with metallic object.
   7. Discuss a news story where the victim dies a horrible death due to electrocution because of unsafe practices. (Look one up on the internet. There are plenty.)
      
4. This discussion should take the entire class period.

Days 3-4

1. Break up the class in groups of 2-3 students each. In a classroom setting, have the students form a circle with their desks. The instructor can be in the middle of this circle and easily assist and monitor all the groups quickly. In a lab setting with lab tables, this may be difficult.
2. The instructor should build a circuit on a breadboard and have the student follow along. Explain why the connections that are made are made.
3. Show the students how to use the multi-meters to measure resistance and voltage.
4. Have the students complete Lab1 of this module.
5. Assist the students.
6. When all the students are finished with the Lab1, go over the lab and explain the expected results and discuss the last question.

Expected Results:

1. This module should familiarize the students with electronics theory.
2. They should be able to use a multi-meter.
3. They should be able to build circuits using the breadboard.S
4. They should understand the relationship between voltage, current, and resistance.

Note of Caution: Students will try to connect the LED to directly to the battery. This will damage the LED. Monitor students as build the circuit so that they do not do this.

Session 4: Introduction to Digital Logic

Prerequisites: Basics of Electronic Circuits module, Number Systems module

Duration: 4-5 Days

Introduction:

This module will expose students to the theory of digital electronics. This module should be used in preparation of the module for building the 2- bit adder circuit. This module will present the theory behind digital electronics and enable the students to experiment with the logic gates.

Objectives:

1. Students grasp the logic theory that gives rise to digital electronics.
2. Students use breadboards to build digital circuits.

Associated Maine Learning Results:

Mathematics

A. NUMBERS AND NUMBER SENSE
1) Describe the structure of the real number system and identify its appropriate applications and limitations.
B. COMPUTATION
2) Explain operations with number systems other than base ten.
G. PATTERNS, RELATIONS, FUNCTIONS
2) Translate and solve a real-life problem using symbolic language.
H. ALGEBRA CONCEPTS
4) Analyze and explain situations using symbolic representations.
K. MATHEMATICAL COMMUNICATION
1) Restate, create, and use definitions in mathematics to express understanding, classify figures, and determine the truth of a proposition or argument.

Science and Technology

J. INQUIRY AND PROBLEM SOLVING
2) Verify, evaluate, and use results in a purposeful way. This includes analyzing and interpreting data, making predictions based on observed patterns, testing solutions against the original problem conditions, and formulating additional questions.
4) Design and construct a device to perform a specific function, then redesign for improvement (e.g., performance, cost).
K. SCIENTIFIC REASONING
3) Develop generalizations based on observations.
5) Produce inductive and deductive arguments to support conjecture.

Required Equipment:

• GK-12 Sensors! Electronic Kits (each kit contains logic gates, dip switches, resistors, and LEDs, and other material)
• "Introduction to Digital Electronics" and "GK-12 Sensors! Breadboard Tips and Techniques for Digital Circuit Construction" handouts
• Power strip
• Extension cord

Procedure:

Days 1-2

1. Students learn best when they interact directly with the material to be covered. Print out enough copies of the "Introduction to Digital Electronics" and "GK-12 Sensors! Breadboard Tips and Techniques for Digital Circuit Construction" handouts for every student in the class.
2. During the class, have the students read aloud from the "Introduction to Digital Electronics" handout . In order to move the reader around the room as quickly as possible, have every other student read a paragraph out loud. Since the reader is moved quickly around the room, the students will be more attentive. Once the reader has moved around the class, the students who were skipped can read now.
3. Work out the examples in the handout with the students.
4. Ask students to complete the exercises.

Days 3-4

1. Have the class form groups of 2-3 students each. In a classroom setting, have the students form a circle with their desks. The instructor can be in the middle of this circle and easily assist and monitor all the groups quickly. In a lab setting with lab tables, this may be difficult.
2. Plug the extension cord in to a wall socket and connect it to the power strip. Place the power strip in the circle of the tables so that all the groups can plug their power transformers can be connected easily.
3. In addition, you can use the power switch on the power strip to control when the students have power and when they don’t.
4. Assign a Digital Electronic Kit to each group.
5. Show the students how to connect the dip switch and the resistor network pack. Make sure that every one has wired this properly, otherwise this will cause many problems later. Check this document for more information on proper setup.
6. Show the students how to connect an Inverter gate properly. E.g. power, ground, inputs, and outputs. Use inputs from the dip switch and connect an LED to the output. Show them how when a logic “1” or true is entered on the dip switch, a logic “0” or false is outputted.
7. Have the students learn how to wire up the AND, OR, and XOR gates.
8. Use the dip-switch to input logic values to the circuit and use an LED to display the results of the logic operation.

Day 5

1. Form the groups of the day before.
2. The students should now know how to hook up the logic gates properly. Have them complete a Digital Electronics Lab Worksheet.

Expected Results:

1. This module should familiarize students with digital electronics theory.
2. Students should be able to connect logic gates properly.
3. Students should be able to translate a logic statement to a logic diagram and then a logic circuit.
4. Students should be able to build logic circuits using the logic gates.

Notes of Caution:

1. Expect to be busy debugging circuits. Students may wire their circuits incorrectly.
2. Note to GK-12 Sensors! Fellows: The logic gates require 5V power and input. However, the transformer in the GK-12 Sensors! Electronics Kit outputs an unregulated 8V. The voltage changes as more and more current is drawn from the transformer. In order to provide for the 5V use the modified power-connector/voltage regulator part. The power-connector for the transformer and the voltage regulator have been hot glued together such that when it is plugged in to the breadboard, only 5 Volts appears on the breadboard. Use this part.
3. If the power and ground on the logic gates are switched or are connected to the input/output pins directly, the logic gate may “burn up.” In order to prevent this, have students build their circuits and then inspect them. After making sure that they are properly wired, okay students to power them up.

Session 5: The Ultimate 2-Bit Binary Adder Circuit

Prerequisites: Basics of Electronic Circuits module, Number Systems module,
Introduction to Digital Logic module

Duration: 3-4 Days

Introduction:

This module will help students to grasp how computer and digital electronics operate. This module should be presented after the two previous modules associated with digital electronics. In this module students will be given a circuit diagram for a 2-bit adder and they are to implement it on the bread-board. This module assumes that the students have a good grasp of reading logic circuit diagrams and they are able to build circuits from those diagrams. This will be a very long module to cover, so be sure that you have enough time to work on it. The recommendeded way of completing this module is on consecutive days so that students do not forget the material between intervening days.

Objectives:

1. Students gain an intuition on how computers/digital electronics work.
2. Students be able to read and implement a logic circuit diagram.

Associated Maine Learning Results:

Mathematics

A. NUMBERS AND NUMBER SENSE
1) Describe the structure of the real number system and identify its appropriate applications and limitations.
B. COMPUTATION
2) Explain operations with number systems other than base ten.
G. PATTERNS, RELATIONS, FUNCTIONS
2) Translate and solve a real-life problem using symbolic language.
H. ALGEBRA CONCEPTS
3) Formulate and solve equations and inequalities.
4) Analyze and explain situations using symbolic representations.
K. MATHEMATICAL COMMUNICATION
1) Restate, create, and use definitions in mathematics to express understanding, classify figures, and determine the truth of a proposition or argument.

Science and Technology

J. INQUIRY AND PROBLEM SOLVING
2) Verify, evaluate, and use results in a purposeful way. This includes analyzing and interpreting data, making predictions based on observed patterns, testing solutions against the original problem conditions, and formulating additional questions.
K. SCIENTIFIC REASONING
5) Produce inductive and deductive arguments to support conjecture.

Required Equipment:

• GK-12 Electronic Kits (Kit contains logic gates, dip switches, resistors, and LEDs, and other material)
• Introduction to Digital Electronics handout
• Ripple Adder Handout
• Ripple Adder 2 Handout
• Power strip
• Extension cord

Procedure:

Day 1

1. Review the material in the Introduction to Digital Electronics handout with students, specifically focusing on the adder circuit discussed at the end of the handout.
2. Review the Ripple Adder handout. Work thorough the exercises.

Days 2-3

1. Break up the class in groups of 2-3 students each. In a classroom setting, have the students form a circle with their desks. The instructor can be in the middle of this circle and easily assist and monitor all the groups quickly. In a lab setting with lab tables, this may be difficult.
2. Plug the extension cord in to a wall socket and connect it to the power strip. Place the power strip in the circle of the tables so that all the groups can plug their power transformers can be connected easily.
3. In addition, you can use the power switch on the power strip to control when the students have power and when they don’t.
4. Assign a Digital Electronic Kit to each group.
5. The students should know how to wire the dip switch and the resistor network pack. See the Introduction to Digital Logic module.
6. Give each group of students a copy of Ripple Adder 2 handout and tell them to implement the adder circuit.

Day 4

1. The adder circuits of those groups of students who have gotten it to work can be connected together to form a much larger adder circuit. Each group of student only builds a 2-bit adder, however, if four or five groups get their circuits working, then an eight or ten bit adder can be built. An eight bit adder circuit can adder two numbers ranging from 0 – 255.
2. The adder circuits can be connected together by connecting the Carry out lines from the last adder to the Carry in lines of the first adder of another group’s circuit.
3. Use only one power supply. All the ground and power lines need to be connected together.
4. Compute the sum of two numbers on the adder circuit.
5. Work out the sum on an overhead projector or the board and show the students that the adder circuit outputs the correct result. Show the sum operation in both binary and decimal.

Expected Results:

1. Once this module is completed the students should have an intuition of how computers/digital systems operate.
2. If the Program Compilation and Execution module was also used in this class, then mention how program statements are compiled into opcode which can be represented as binary numbers and executed on processors.
3. They should be able to connect logic gates properly to form an adder circuit.
4. They should be able to explain the working of the adder circuit and how the sum and the carry values are generated.

Notes of Caution:

1. Expect to be busy debugging circuits. Students may wire up their circuits incorrectly.
2. Note to GK-12 Sensors! Fellows: The logic gates require 5V power and input. However, the transformer in the GK-12 Electronics Kit outputs an unregulated 8V. The voltage changes as more and more current is drawn from the transformer. In order to provide for the 5V use the modified power-connector/voltage regulator part. The power-connector for the transformer and the voltage regulator have been hot glued together such that when it is plugged in to the breadboard, only 5 Volts appears on the breadboard. Use this part.
3. If the power and ground on the logic gates are switched or are connected to the input/output pins directly, the logic gate may “burn up.” In order to prevent this, have the students build their circuit and then inspect it. After making sure that it is properly wired, allow them to power it up.
4. Each chip contains more than one logic gate. The logic gates on the same chip can be used for the same adder. However, for ease of wiring and debugging use separate sets of chips for each adder.
5. The complexity of the circuit being built may make it difficult to debug a circuit during class. Some students may have obvious problems which can be solved quickly, however, there will be students who will have non-obvious problems with their circuits. At the end of the day take all those circuits that do not work home and debug them. There will not be enough time to debug every circuit during the class.
   

Example of a circuit implementation:

The two adder circuits are separated. The first adder is on the left and the second adder on the right. The red wires are used to feed the Carry Out of the first adder to the second adder.