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IT: [Computer Programming]: [Boolean Logic] Plan Copyright © Texas Education Agency, 2013 1 Lesson Plan Course Title: Computer Programming Session Title: Boolean Logic Lesson Duration: 2-3 hours Performance Objective: Upon completion of this assignment, the student will be able to apply Boolean logic in problem solving and identify logic terms and explain the logic operators. Specific Objectives: Recognize and explain the function of Boolean logical operators: NOT, AND, OR Generate truth tables for logic operators Given a logic statement, identify the correct locations on Venn diagrams Match shaded Venn diagrams to logic statements Given logical conditions in sample code, predict the outcome Apply Boolean logic to create a decision-making structure Identify logic terms and explain the logic operators Preparation TEKS Correlations: 130.276(c) 1.E – solve problems and think critically 4.B – identify input and output requirements 4.C – identify system processing requirements 6.B – perform a logical design 6.C – use algorithmic concepts 6.D – identify constraints 7.E – compare computed results with anticipated results to determine the reasonableness of the solutions PRESENTATIONInstructor/Trainer References: Content Developer Knowledge Java Software Solutions for AP Computer Science, by Lewis, Loftus, & Cocking, copyright 2004, Pearson Education, Inc. Introduction to Computer Science using Java, by Liberty, Quirk & Weiss, copyright 2005, Glencoe McGraw-Hill Instructional Aids: Lab File: LogicObservation.java Handout: Observing Boolean Logic & KEY Lab File: LogicObservation2.java Handout: Observing Boolean Logic2 & KEY Presentation: Boolean Logic

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Page 1: Model Instruction Plandata.cteunt.org/.../2-06-boolean-logic/02.06-boolean-logic.pdf · Recognize and explain the function of Boolean logical operators: NOT, AND, OR Generate truth

IT: [Computer Programming]: [Boolean Logic] Plan Copyright © Texas Education Agency, 2013

1

Lesson Plan Course Title: Computer Programming

Session Title: Boolean Logic

Lesson Duration: 2-3 hours

Performance Objective: Upon completion of this assignment, the student will be able to apply Boolean logic in

problem solving and identify logic terms and explain the logic operators.

Specific Objectives: Recognize and explain the function of Boolean logical operators: NOT, AND, OR Generate truth tables for logic operators Given a logic statement, identify the correct locations on Venn diagrams Match shaded Venn diagrams to logic statements Given logical conditions in sample code, predict the outcome Apply Boolean logic to create a decision-making structure Identify logic terms and explain the logic operators

Preparation

TEKS Correlations: 130.276(c) 1.E – solve problems and think critically 4.B – identify input and output requirements 4.C – identify system processing requirements 6.B – perform a logical design 6.C – use algorithmic concepts 6.D – identify constraints 7.E – compare computed results with anticipated results to determine the reasonableness of

the solutions

PRESENTATIONInstructor/Trainer

References: Content Developer Knowledge Java Software Solutions for AP Computer Science, by Lewis, Loftus, & Cocking, copyright

2004, Pearson Education, Inc. Introduction to Computer Science using Java, by Liberty, Quirk & Weiss, copyright 2005,

Glencoe McGraw-Hill Instructional Aids: Lab File: LogicObservation.java Handout: Observing Boolean Logic & KEY Lab File: LogicObservation2.java

Handout: Observing Boolean Logic2 & KEY Presentation: Boolean Logic

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Handout: Boolean Logic & KEY Lab File : EasyUsingLogic.java & EasyUsingLogicKEY.java Handout: Boolean Logic Review & KEY Handout: Boolean Logic Quiz A & B & KEYS Handout: Boolean Logic Test and Re-Test & KEYS Presentation: Digital Gates Handout: Gates and Boolean Expressions & KEY Lab File: GetUp.java

Materials Needed: • Copies of instructional aides • Pen or pencil

Equipment Needed: Each student will need access to a computer with Java installed

Learner

The learner should have understanding of simple Java code, including system output and IF statements.

Introduction

MI Introduction (LSI Quadrant I):

The instructor begins a group discussion about practical decisions that students make on their own, by having students list various choices and decisions that they make throughout the day, beginning with the choice of whether or not to get out of bed. Have students also identify what factors they base their decisions on. In programming, the factors that are evaluated to make a decision are known as the ‘condition.’ Have students critique hypothetical situations in which people make good and bad decisions. Have students summarize characteristics of effective decision making.

Have students come to the board to draw a simple decision tree that has branches for each option that can be chosen. For example, the question ‘should I get up?’ has two possible options: the ‘yes’ branch leads to other possible questions, like ‘should I eat breakfast?;’ the ‘no’ branch leads right back to the condition that existed prior to asking the question ‘should I get up?’

Outline

MI Outline (LSI Quadrant II): Instructor Notes:

The instructor presents the ‘Boolean Logic’ Presentation. Students follow along using the ‘Boolean Logic Guided Notes.’ The instructor can pause at any point to expand the discussion or clarify concepts. Terms & Concepts presented: • Boolean background

The Presentation and guided notes can also be used by students who were absent and trying to catch up. It can also be used as a review. The ‘Boolean Logic Guided Notes KEY’ helps to assess

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• Boolean Operators (AND, OR, NOT) • Order of operations • Venn diagrams • Truth Tables • Evaluating Boolean expressions • Using Boolean expressions in Java

how well the student followed and comprehended the presentation.

The lab handout ‘Observing Boolean Logic’ uses the Java file ‘LogicObservation.java,’ and is intended for students to observe and analyze the function of Boolean expressions in Java code. Students observe and analyze the following: • Declaration of Boolean variables • Evaluation of Boolean conditions • Truth table values as they occur in Java code for

NOT, OR, AND • Combinations of Boolean variable values

Students can work alone or in pairs to complete the lab, but each should turn in their own paper. The questions on the paper match sections in the Java file.

Observation labs do not require much code modification. Students observe and analyze the operation of existing code. The lab handout ‘Observing Boolean Logic 2’ uses the Java file ‘LogicObservation2.java,’ and is intended for students to observe and analyze the function of Boolean expressions in Java code. Students observe and analyze the following: • Relational operators • Setting Boolean variables and values • Using Boolean variables

Students can work alone or in pairs to complete the lab, but each should turn in their own paper.

Application

MI Guided Practice (LSI Quadrant III):

The lab file ‘LogicPractice.java’ contains commented instructions and code samples. The student copies and pastes sample code, making minor modifications to build confidence in using Boolean logic in Java. Students may work in pairs, but each student should complete their own lab file. Successful completion of the lab is evident when the student’s code prints different messages, depending on the age and gender answers given during prompts in the program. It is possible to have more than one message.

The four cases of the lab are as follows:

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• If the age is between 14 and 18, the message should say “in High School” • If the age is more than 15 and the gender is male, the message should say “You

should be shaving” • If the gender is female and the age is more than 21, the message should say

“You get an insurance break” • If the age is below 5 or above 55, the message should say “You get a discount”

MI Independent Practice (LSI Quadrant III):

The lab file ‘EasyUsingLogic.java’ contains commented instructions and code samples. The student can use samples in the code, or from previous labs, to complete objectives in the instructions. At this point students should be able to work without a lab partner. This lab simulates ticket price calculations at a ticket booth. Successful completions of the lab are evident when the student’s code prints different messages, depending on the age, row, and coupon answers given during prompts in the program. It is possible to have more than one message. The cases of the lab are as follows: • If the age is below 12, the row is not the front row, and there is no coupon; the

message should say “$5” • If the age is below 12, the row is not the front row, and there is a coupon; the

message should say “$3” • If the age is below 12, and the row is the front row; the message should say “$8”

whether or not there is a coupon. • If the age is 12 or more, the row is not the front row, and there is no coupon; the

message should say “$10” • If the age is 12 or more, the row is not the front row, and there is a coupon; the

message should say “$8” • If the age is 12 or more, and the row is the front row; the message should say

“$12”, whether or not there is a coupon.

Summary

MI Review (LSI Quadrants I and IV):

The worksheet ‘Logic Review’ helps students confirm their understanding of truth tables, Venn diagrams, and Boolean expressions. After grading have a group discussion to explain each problem.

Evaluation

MI Informal Assessment (LSI Quadrant III):

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The students show their completed labs to the teacher, who may also ask pointed questions about how certain sections of the code work. The amount of help students need in completing a lab may indicate their degree of understanding and application of the material.

MI Formal Assessment (LSI Quadrant III, IV):

Logic Quiz & Logic Test let students demonstrate mastery of Boolean expressions, Venn diagrams, truth tables, and the application of Boolean logic in simple Java code.

Extension

MI Extension/Enrichment (LSI Quadrant IV):

Have students complete the ‘GetUp.java’ lab file. Students create a series of questions to help them decide whether or not to get up in the morning. Questions could include such factors as ‘is it a week day?’ or ‘is it earlier than 7:00am?’ The code will also need to contain Boolean decision-making to indicate if the student will, in fact, get up, based on the answers provided. Students may copy blocks of code from previous labs and modify it as needed. Successful completion of the lab is evident when the student’s code prints different messages, depending on the three questions that are designed by the student. Testing the students’ code will requiring several attempts using different answers. Additional Enrichment includes presenting the Presentation ‘Digital Gates’ which explains the connection between Boolean logic and digital schematic, including the following concepts: • How True and False relate to actual voltages in electronics • Recognizing Gate symbols as they are used in schematics • An explanation of how each of the basic gates works • The abbreviation of the NOT gate symbol as a circle • Schematics can be converted to Boolean expressions Students use information from the Presentation to complete the handout ‘Gates and Boolean Expressions.’

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Icon MI Teaching Strategies Personal Development Strategies

Verbal/ Linguistic

Lecture, discussion, journal writing, cooperative learning, word origins

Reading, highlighting, outlining, teaching others, reciting information

Logical/ Mathematical

Problem solving, number games, critical thinking, classifying and organizing, Socratic questioning

Organizing material logically, explaining things sequentially, finding patterns, developing systems, outlining, charting, graphing, analyzing information

Visual/Spatial

Mind-mapping, reflective time, graphic organizers, color-coding systems, drawings, designs, video, DVD, charts, maps

Developing graphic organizers, mind-mapping, charting, graphing, organizing with color, mental imagery (drawing in the mind’s eye)

Musical/ Rhythmic

Use music, compose songs or raps, use musical language or metaphors

Creating rhythms out of words, creating rhythms with instruments, playing an instrument, putting words to existing songs

Bodily/ Kinesthetic

Use manipulatives, hand signals, pantomime, real life situations, puzzles and board games, activities, role-playing, action problems

Moving while learning, pacing while reciting, acting out scripts of material, designing games, moving fingers under words while reading

Intrapersonal

Reflective teaching, interviews, reflective listening, KWL charts

Reflecting on personal meaning of information, studying in quiet settings, imagining experiments, visualizing information, journaling

Interpersonal

Cooperative learning, role-playing, group brainstorming, cross-cultural interactions

Studying in a group, discussing information, using flash cards with other, teaching others

Naturalist

Natural objects as manipulatives and as background for learning

Connecting with nature, forming study groups with like minded people

Existentialist

Socratic questions, real life situations, global problems/questions

Considering personal relationship to larger context

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Name: _______________________ Date: ________________ Period: ________

Observing Boolean Logic Objective: Observe and analyze the function of Boolean logic operators and the outcome of Boolean statements. Instructions: Follow the directions below as you run the program LogicObservation.java. Record your observations and analysis below. #1 BOOLEAN VALUES

1. Look at the statement above section #1 where the Boolean variables are declared. What is the value of ‘b’? [ true / false / a / b ]

2. When the variable ‘a’ is put in System.out.println(), what is printed? [ true / false / a

/ b ]

3. When any variable is put in System.out.println(), what is printed? [ the name of the variable / the value of the variable / cannot be determined ]

#2 BOOLEAN CONDITIONS

4. In the statement ‘ if (a) ‘ , the condition evaluates to the value [ true / false / a / b ].

5. The statement after ‘ if (b) ‘ , [ does / does not ] execute because the value of ‘b’ is [ true / false ].

6. The statement after ‘ if (false) ‘ does not print because…

a. the value ‘false’ is not valid for a condition. b. you must put a Boolean variable in the condition. c. the condition evaluates to false. d. it is not a valid statement.

7. If the value of an if statement’s condition evaluates to true, then the statement that

follows [ will / will not ] execute. #3 NOT

8. The expression ‘ !a ‘ evaluates to… [ a / true / false / 0 ].

9. The expression ‘ !false ‘ evaluates to… [ a / true / false / 0 ].

10. The NOT operator ‘!’ does which of the following? a. Makes a true value false and a false value true b. Makes the value one less than it was c. Shows the value instead of the name

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#4 AND

11. ( true && true ) evaluates to [ true / false ].

12. ( true && false ) evaluates to [ true / false ].

13. ( false && true ) evaluates to [ true / false ].

14. ( false && false ) evaluates to [ true / false ].

15. When a true and a false are AND’ed together, like ( true && false) or (false && true), it [ does / does not ] matter if the true value is first.

16. The statement (a && b) is the same as which one?

a. ( true && false ) b. ( true && true ) c. ( false && false )

#5 OR

17. ( true || true ) evaluates to [ true / false ].

18. ( true || false ) evaluates to [ true / false ].

19. ( false || true ) evaluates to [ true / false ].

20. ( false || false ) evaluates to [ true / false ].

21. The statement (a || b) is the same as which one? a. ( true || false ) b. ( true || true ) c. ( false || false)

#6 COMBINING BOOLEAN OPERATORS

22. ( a && !b ) evaluates to [ true / false ].

23. ( !a && b ) evaluates to [ true / false ].

24. ( false || !false ) evaluates to [ true / false ].

25. ( !!!false ) evaluates to [ true / false ].

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Name: _______________________ Date: ________________ Period: ________

Observing Boolean Logic KEY Objective: Observe and analyze the function of Boolean logic operators and the outcome of Boolean statements. Instructions: Follow the directions below as you run the program LogicObservation.java. Record your observations and analysis below. #1 BOOLEAN VALUES

1. Look at the statement above section #1 where the Boolean variables are declared. What is the value of ‘b’? [ true / false / a / b ]

2. When the variable ‘a’ is put in System.out.println(), what is printed? [ true / false / a

/ b ]

3. When any variable is put in System.out.println(), what is printed? [ the name of the variable / the value of the variable / cannot be determined ]

#2 BOOLEAN CONDITIONS

4. In the statement ‘ if (a) ‘ , the condition evaluates to the value [ true / false / a / b ].

5. The statement after ‘ if (b) ‘ , [ does / does not ] execute because the value of ‘b’ is [ true / false ].

6. The statement after ‘ if (false) ‘ does not print because…

a. the value ‘false’ is not valid for a condition. b. you must put a boolean variable in the condition. c. the condition evaluates to false. d. it is not a valid statement.

7. If the value of an if statement’s condition evaluates to true, then the statement that

follows [ will / will not ] execute. #3 NOT

8. The expression ‘ !a ‘ evaluates to… [ a / true / false / 0 ].

9. The expression ‘ !false ‘ evaluates to… [ a / true / false / 0 ].

10. The NOT operator ‘!’ does which of the following? a. Makes a true value false and a false value true b. Makes the value one less than it was c. Shows the value instead of the name

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#4 AND

11. ( true && true ) evaluates to [ true / false ].

12. ( true && false ) evaluates to [ true / false ].

13. ( false && true ) evaluates to [ true / false ].

14. ( false && false ) evaluates to [ true / false ].

15. When a true and a false are AND’ed together, like ( true && false) or (false && true), it [ does / does not ] matter if the true value is first.

16. The statement (a && b) is the same as which one?

a. ( true && false ) b. ( true && true ) c. ( false && false )

#5 OR

17. ( true || true ) evaluates to [ true / false ].

18. ( true || false ) evaluates to [ true / false ].

19. ( false || true ) evaluates to [ true / false ].

20. ( false || false ) evaluates to [ true / false ].

21. The statement (a || b) is the same as which one? a. ( true || false ) b. ( true || true ) c. ( false || false)

#6 COMBINING BOOLEAN OPERATORS

22. ( a && !b ) evaluates to [ true / false ].

23. ( !a && b ) evaluates to [ true / false ].

24. ( false || !false ) evaluates to [ true / false ].

25. ( !!!false ) evaluates to [ true / false ].

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Name: _________________________ Date: ____________________ Period: _____

Observing Boolean Logic2 Objective: Observe and analyze the function of Boolean logic operators and relational operators. Instructions: Follow the directions below as you run the program LogicObservation2.java. Record your observations and analysis below. Circle all correct answers for each question. #1 RELATIONAL OPERATORS

1. In the if statement, if ( age > 12 && age <20), which of the following values of age would make the condition true? There may be more than one. [ 21 / 12 / 15 / 6 / no value could make the condition true ]

2. When the condition above is evaluated, which are evaluated first, the relational

operators ( > < ) or the Boolean operator ( && )? [ relational / Boolean ]

3. In the if statement, if ( age < 16 || age > 72), which of the following values of age would make the condition true? There may be more than one. [ 15 / 25 / 78 / no value could make the condition true ]

4. In the if statement if ( !(age <18) ) , the condition is true if age is [ less than 18, greater

than 18 ]. #2 SETTING BOOLEAN VARIABLES

5. Look at the code in section #2. If the user enters a 13 for the ‘gender’ variable, then the value of isMale will be [ 13 / 1 / 0 / true / false ].

6. Look at the code in section #2. In general, what happens?

a. The user enters a Boolean value that may change the original value of a Boolean variable.

b. The user enters a numeric value that may change the original value of a Boolean variable.

7. Look at the code in section #2. If the user enters a 1 for the ‘hungry’ variable, then the

value of isHungry will be [ -1 / 1 / 0 / true / false ].

8. Look at the code in section #2. If the user enters a 2 for the ‘senior’ variable, then the value of isSenior will be [ 2 / 1 / 0 / true / false ].

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9. Look at the code in section #2. Which of the following statements are true about the

Boolean variables? There may be more than one. a. They are declared and initialized inside of the if statements. b. They are declared and initialized outside of the if statements. c. The only way they can have a value assigned is if the condition of the if

statement is true; otherwise they will not have a value. #3 USING BOOLEAN VARIABLES

10. The if statement if (isSenior && age < 18) will still evaluate to true, even if isSenior is false, as long as age is less than 18. [ true / false ]

11. The if statement if (!isMale && age < 12) only evaluates to true for girls under the age

of 12. [ true / false ]

12. The if statement if (isHungry && isSenior) evaluates to true for juniors who are not hungry. [ true / false ]

13. The if statement if (age > 16 || !isSenior) evaluates to true for seniors who are 17. [ true

/ false ]

14. The if statement if (!isMale && isSenior) only evaluates to true for female seniors. [ true / false ]

15. Write your own if condition that prints “Lunch” either for girls or non-seniors.

if ( ) { System.out.println(“Lunch”); }

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Name: _________________________ Date: ____________________ Period: _____

Observing Boolean Logic2 KEY Objective: Observe and analyze the function of Boolean logic operators and relational operators. Instructions: Follow the directions below as you run the program LogicObservation2.java. Record your observations and analysis below. Circle all correct answers for each question. #1 RELATIONAL OPERATORS

1. In the if statement, if ( age > 12 && age <20), which of the following values of age would make the condition true? There may be more than one. [ 21 / 12 / 15 / 6 / no value could make the condition true ]

2. When the condition above is evaluated, which are evaluated first, the relational

operators ( > < ) or the Boolean operator ( && )? [ relational / boolean ]

3. In the if statement, if ( age < 16 || age > 72), which of the following values of age would make the condition true? There may be more than one. [ 15 / 25 / 78 / no value could make the condition true ]

4. In the if statement, if ( !(age <18) ) , the condition is true if age is [ less than 18, greater

than 18 ]. #2 SETTING BOOLEAN VARIABLES

5. Look at the code in section #2. If the user enters a 13 for the ‘gender’ variable, then the value of isMale will be [ 13 / 1 / 0 / true / false ].

6. Look at the code in section #2. In general, what happens?

a. The user enters a Boolean value that may change the original value of a Boolean variable.

b. The user enters a numeric value that may change the original value of a Boolean variable.

7. Look at the code in section #2. If the user enters a 1 for the ‘hungry’ variable, then the

value of isHungry will be [ -1 / 1 / 0 / true / false ].

8. Look at the code in section #2. If the user enters a 2 for the ‘senior’ variable, then the value of isSenior will be [ 2 / 1 / 0 / true / false ].

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9. Look at the code in section #2. Which of the following statements are true about the Boolean variables? There may be more than one.

a. They are declared and initialized inside of the if statements. b. They are declared and initialized outside of the if statements. c. The only way they can have a value assigned is if the condition of the if

statement is true; otherwise they will not have a value. #3 USING BOOLEAN VARIABLES

10. The if statement if (isSenior && age < 18) will still evaluate to true, even if isSenior is false, as long as age is less than 18. [ true / false ]

11. The if statement if (!isMale && age < 12) only evaluates to true for girls under the age

of 12. [ true / false ]

12. The if statement if (isHungry && isSenior) evaluates to true for juniors who are not hungry. [ true / false ]

13. The if statement if (age > 16 || !isSenior) evaluates to true for seniors who are 17. [

true / false ]

14. The if statement if (!isMale && isSenior) only evaluates to true for female seniors. [ true / false ]

15. Write your own if condition that prints “Lunch” either for girls or non-seniors.

if ( ! isMale || ! isSenior) { System.out.println(“Lunch”); }

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Name: _________________________ Date: ____________________ Period: _____

Guided Notes: Boolean Logic Objective: Become familiar with Boolean operators, logic statements and Venn Diagrams. Instructions: Answer the questions below as you view the presentation.

1. Which would be true for a brown-eyed girl? [ Brown-eyed AND male / Brown-eyed OR male ]

2. Write the Java Boolean operators for the following

a. AND ___ b. OR ___ c. NOT ___

3. Which of the following is true for a short red-head? [ !Tall && Blonde / !(tall && blonde) ]

4. Write numbers in the space to indicate the order in which they should be considered.

a. _ _ _ AND && b. _ _ _ NOT ! c. _ _ _ OR || d. _ _ _ PARENTHESIS ( )

5. Color in the following Venn diagrams.

A || B A && B !A !A && B

6. Complete your own truth tables below

A B A&&B T T T F F T F F

A B A||B T T T F F T F F

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A B !B T T T F F T F F

A B A || !B T T T F F T F F

7. If blonde=true, what is (!blonde)? [ blonde / true / false ] 8. What generalization can you make about the AND (&&) truth table? There may be more

than one correct statement. a. If any variable is TRUE, the result will be TRUE. b. If any variable is FALSE, the result will FALSE. c. All variables must be FALSE to make the result FALSE. d. All variables must be TRUE to make the result TRUE.

9. What generalization can you make about the OR (||) truth table? There may be more than one correct statement.

a. If any variable is TRUE, the result will be TRUE. b. If any variable is FALSE, the result will FALSE. c. All variables must be FALSE to make the result FALSE. d. All variables must be TRUE to make the result TRUE.

10. Shade in the Venn Diagrams

A || ! B A && !B !A && !B

11. What do the values need to be to make the Boolean expression “x && !y”, evaluate to

True? a. x = true, y = true b. x = false, y = true c. x = true, y = false

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Name: _________________________ Date: ____________________ Period: _____

Guide Notes: Boolean Logic KEY Objective: Become familiar with Boolean operators, logic statements and Venn Diagrams. Instructions: Answer the questions below as you view the presentation.

1. Which would be true for a brown-eyed girl? [ Brown-eyed AND male / Brown-eyed OR male ]

2. Write the Java Boolean operators for the following

a. AND && b. OR || c. NOT !

3. Which of the following is true for a short red-head? [ !Tall && Blonde / !(tall && blonde) ]

4. Write numbers in the space to indicate the order in which they should be considered.

a. _ 3 _ _ AND && b. _ 2 _ _ NOT ! c. _ 4 _ _ OR || d. _ 1 _ _ PARENTHESIS ( )

5. Color in the following Venn diagrams.

A || B A && B !A !A && B

6. Complete your own truth tables below

A B A&&B T T T T F F F T F F F F

A B A||B T T T T F T

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F T T F F F

A B !B T T F T F T F T F F F T

A B A || !B T T T T F T F T F F F T

7. If blonde=true, what is (!blonde)? [ blonde / true / false ] 8. What generalization can you make about the AND (&&) truth table? There may be more

than one correct statement. a. If any variable is TRUE, the result will be TRUE. b. If any variable is FALSE, the result will FALSE. c. All variables must be FALSE to make the result FALSE. d. All variables must be TRUE to make the result TRUE.

9. What generalization can you make about the OR (||) truth table? There may be more than one correct statement.

a. If any variable is TRUE, the result will be TRUE. b. If any variable is FALSE, the result will FALSE. c. All variables must be FALSE to make the result FALSE. d. All variables must be TRUE to make the result TRUE.

10. Shade in the Venn Diagrams A || ! B A && !B !A && !B

11. What do the values need to be to make the Boolean expression “x && !y”, evaluate to

True? a. x = true, y = true b. x = false, y = true c. x = true, y = false

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Review Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answers for each question. The following are Boolean variables used to describe a sandwich: P is for pepperoni, C is for cheese, M is for Mushrooms.

1. A pizza with either pepperoni or mushrooms is…( P || M ) / ( P && M ) / ( !P || !C ) / ( P || C )

2. A pizza with neither pepperoni nor cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / ( P

|| C )

3. A pizza with mushrooms but no cheese is…( M && ! C) / ( !M && !C ) / ( M || !C ) / !( M || C )

4. Shade the Venn diagram below for ( !A || B )

5. Shade the Venn diagram below for ( A && !B)

boolean x = false; int age = 7; while ( !x && age > 2) { if ( age = = 4 ) x = !x; age --; } 6. When the loop above finishes, the value of age will be? ____

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Complete the truth tables below. A B A && B True True True False False True False False A B A || B True True True False False True False False A B !A || B True True True False False True False False A B !A && ! B True True True False False True False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Review KEY Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answers for each question. The following are Boolean variables used to describe a sandwich: P is for pepperoni, C is for cheese, M is for Mushrooms

1. A pizza with either pepperoni or mushrooms is…( P || M ) / ( P && M ) / ( !P || !C ) / ( P || C )

2. A pizza with neither pepperoni nor cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / ( P

|| C )

3. A pizza with mushrooms but no cheese is…( M && ! C) / ( !M && !C ) / ( M || !C ) / !( M || C )

4. Shade the Venn diagram below for ( !A || B )

5. Shade the Venn diagram below for ( A && !B)

boolean x = false; int age = 7; while ( !x && age > 2) { if ( age = = 4 ) x = !x; age --; } 6. When the loop above finishes, the value of age will be? _3__

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Complete the truth tables below. A B A && B True True True True False False False True False False False False A B A || B True True True True False True False True True False False False A B !A || B True True True True False False False True True False False True A B !A && ! B True True False True False False False True False False False True

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Quiz A Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answer for each question. The following are Boolean variables used to describe a sandwich: P is for pickles, B is for Bacon, C is for cheese, M is for mustard.

1. A sandwich with either pickles or cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / ( P || C )

2. A sandwich with neither pickles nor cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / !(

P || C )

3. A sandwich with mustard but no cheese is…( M && ! C) / ( !M && !C ) / ( M || !C ) / !( M || C )

4. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

5. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

6. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

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7. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B) boolean x = true; int age = 1; while ( x && age < 7) { if ( age = = 4 ) x = !x; age ++; }

8. When the loop above finishes, the value of age will be [ 1 / 4 / 5 / 7 / 8 ] Complete the truth tables below. A B A && B True True True False False True False False A B A || B True True True False False True False False A B !A || B True True True False False True False False A B A && ! B True True True False False True False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Quiz A KEY Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answer for each question. The following are Boolean variables used to describe a sandwich: P is for pickles, B is for Bacon, C is for cheese, M is for mustard.

1. A sandwich with either pickles or cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / ( P || C )

2. A sandwich with neither pickles nor cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / !(

P || C )

3. A sandwich with mustard but no cheese is…( M && ! C) / ( !M && !C ) / ( M || !C ) / !( M || C )

4. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

5. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

6. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

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7. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B) boolean x = true; int age = 1; while ( x && age < 7) { if ( age = = 4 ) x = !x; age ++; }

8. When the loop above finishes, the value of age will be [ 1 / 4 / 5 / 7 / 8 ] Complete the truth tables below. A B A && B True True True True False False False True False False False False A B A || B True True True True False True False True True False False False A B !A || B True True True True False False False True True False False True A B A && ! B True True False True False True False True False False False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Quiz B Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answer for each question. boolean x = true; int age = 1; while ( x && age < 7) { if ( age = = 4 ) x = !x; age ++; }

1. When the loop above finishes, the value of age will be [ 1 / 4 / 5 / 7 / 8 ] The following are Boolean variables used to describe a sandwich: P is for pickles, B is for Bacon, C is for cheese, M is for mustard.

2. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

3. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

4. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

5. A sandwich with either pickles or cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / ( P || C )

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6. A sandwich with neither pickles nor cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / !( P || C )

7. A sandwich with mustard but no cheese is…( M && ! C) / ( !M && !C ) / ( M || !C ) /

!( M || C )

8. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A || B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

Complete the truth tables below. A B A || B True True True False False True False False A B A && B True True True False False True False False A B A || !B True True True False False True False False A B !A && B True True True False False True False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Quiz B KEY Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answer for each question. boolean x = true; int age = 1; while ( x && age < 7) { if ( age = = 4 ) x = !x; age ++; }

1. When the loop above finishes, the value of age will be [ 1 / 4 / 5 / 7 / 8 ] The following are Boolean variables used to describe a sandwich: P is for pickles, B is for Bacon, C is for cheese, M is for mustard.

2. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

3. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

4. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A ||

B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

5. A sandwich with either pickles or cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / ( P || C )

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6. A sandwich with neither pickles nor cheese is…( B || C ) / ( P && C ) / ( !P || !C ) / !( P || C )

7. A sandwich with mustard but no cheese is…( M && ! C) / ( !M && !C ) / ( M || !C ) /

!( M || C )

8. Circle the correct expression for the Venn diagram above. ( A && B) / ( A || B ) / ( !A || B ) / ( ! A && B ) / ( A && !B) / ( A || ! B) / ( !B)

Complete the truth tables below. A B A || B True True True True False True False True True False False False A B A && B True True True True False False False True False False False False A B A || !B True True True True False True False True False False False True A B !A && B True True False True False False False True True False False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Test Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answers for each question. The following are Boolean variables used to describe a crowd: H = people with hats, M = males, P= people with phones

1. People with either phones or hats. ( H && P ) / ( P && H ) / ( P || H )

2. Women who do not have phones. ( F && !P ) / ( !M && !P ) / ( !M || ! P )

3. Men without hats. ( M || !H) / ( M && !H) / ( !H || M ) Match the descriptions to the Venn diagrams by writing the number of the description in the blank above the diagram.

4. Women who have either hats or phones 5. Women who have hats and phones 6. Men who have both hats and phones 7. Men who have phones 8. Women who have no men 9. Men who have phones but do not have hats 10. Men who have hats 11. Men who have hats but do not have phones 12. Men who don’t have neither phones nor hats

_______ _______ _______ _______ _______ ______ _______

_______

________ _______ ________ _______ ______ _______ Match the logic expressions below with the Venn diagrams above by writing the number of the expression in the blank below the diagram.

13. M && (P && !H) 14. M && P 15. M && (H && !P) 16. M && P && H

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17. M && H 18. !M && (H || P) 19. !M && (H && P) boolean a = true, b = false, c = true; if ( !b ){ System.out.print(b); b = !b; } if (b && a){ c = !a; System.out.print(a); } if (a || !c) { b = !b; System.out.print(b); }

20. When the code above runs, it will print [ truetruetrue / truefalsetrue / truetruefalse /

falsefalsefalse / falsetruefalse / falsetruetrue 21. When the code above finishes running, the value of a is [ true / false ]

22. When the code above finishes running, the value of b is [ true / false ]

23. When the code above finishes running, the value of c is [ true / false ]

Complete the truth tables below. A B A && B True True True False False True False False A B !!!A || B True True True False False True False False A B !A && ! B True True True False False True False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Test KEY Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answer for each question. The following are Boolean variables used to describe a crowd: H = people with hats, M = males, P= people with phones

1. People with either phones or hats ( H && P ) / ( P && H ) / ( P || H )

2. Women who do not have phones ( F && !P ) / ( !M && !P ) / ( !M || ! P )

3. Men without hats ( M || !H) / ( M && !H) / ( !H || M ) Match the descriptions to the Venn diagrams by writing the number of the description in the blank above the diagram.

4. Women who have either hats or phones. 5. Women who have hats and phones 6. Men who have both hats and phones. 7. Men who have phones 8. Women who have no men 9. Men who have phones but do not have hats 10. Men who have hats 11. Men who have hats but do not have phones 12. Men who don’t have neither phones nor hats

_ _11 _ _ _10 _ _ _9 _ _ _7 _ _ _4_ _ _ _ 6 _ _ _5_ _

_ 15_ _ _ _17 _ _ 13_ _ _ _14 _ _ 18_ _ _ 16_ _ _ 19_ _ Match the logic expressions below with the venn diagrams above by writing the number of the expression in the blank below the diagram.

13. M && (P && !H) 14. M && P 15. M && (H && !P) 16. M && P && H

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17. M && H 18. !M && (H || P) 19. !M && (H && P)

boolean a = true, b = false, c = true; if ( !b ){ System.out.print(b); b = !b; } if (b && a){ c = !a; System.out.print(a); } if (a || !c) { b = !b; System.out.print(b); }

20. When the code above runs, it will print [ truetruetrue / truefalsetrue / truetruefalse /

falsefalsefalse / falsetruefalse / falsetruetrue 21. When the code above finishes running, the value of a is [ true / false ]

22. When the code above finishes running, the value of b is [ true / false ]

23. When the code above finishes running, the value of c is [ true / false ]

Complete the truth tables below. A B A && B True True True True False False False True False False False False A B !!!A || B True True True True False False False True True False False True A B !A && ! B True True False True False False False True False False False True

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Re-Test Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answers for each question. The following are Boolean variables used to describe a crowd: G = Girls, I = ID badge, U = Un-tucked shirt

1. Boys with un-tucked shirts ( B && U ) / ( !G && U ) / ( !G || U )

2. Girls with tucked-in shirts and ID badges ( G && !U && I ) / ( G || !U || I ) / ( !G && !U && !I )

3. Boys with no ID badge ( !G || !I ) / ( !G && I ) / ( !G && !I )

Match the descriptions to the Venn diagrams by writing the number of the description in the blank above the diagram.

4. Girls who have ID, and their shirts are tucked-in 5. People with ID and un-tucked shirts 6. Boys who have un-tucked shirts and IDs 7. Girls who have neither IDs, nor un-tucked shirts 8. Girls who have IDs 9. Boys who have either IDs or un-tucked shirts 10. Girls who have either ID or un-tucked shirts 11. Girls who don’t have ID, but they do have un-tucked shirts 12. Girls who have ID and un-tucked shirts

______ ______ ______ ______ _______ _______ _______

______ ______ ______ ______ ______ _______ _______ Match the logic expressions below with the Venn diagrams above by writing the number of the expression in the blank below the diagram.

13. G && ( I || U ) 14. !G && ( I && U ) 15. ( I && U ) 16. G && ( I && ! U ) 17. G && ( I && U )

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18. G && ( ! I && ! U ) 19. G && I

boolean a = false, b = false, c = true; if ( !a ){ System.out.print(a); a = !b; } if (!b && a){ c = !a; System.out.print(!c); } if (a || !c) { b = !b; System.out.print(b); }

20. When the code above runs, it will print [ truetruetrue / truefalsetrue / truetruefalse / falsefalsefalse / falsetruefalse / falsetruetrue

21. When the code above finishes running, the value of a is [ true / false ]

22. When the code above finishes running, the value of b is [ true / false ]

23. When the code above finishes running, the value of c is [ true / false ]

Complete the truth tables below. A B !A && !B True True True False False True False False A B !A || !B True True True False False True False False A B A || ! B True True True False False True False False

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Name: _________________________ Date: ____________________ Period: _____

Boolean Logic Re-Test KEY Objective: Demonstrate understanding of Boolean operators and their effect on condition evaluations. Instructions: Examine the code below as you choose all correct answer for each question. The following are Boolean variables used to describe a crowd: G = Girls, I = ID badge, U = Un-tucked shirt

1. Boys with un-tucked shirts. ( B && U ) / ( !G && U ) / ( !G || U )

2. Girls with tucked-in shirts and ID badges. ( G && !U && I ) / ( G || !U || I ) / ( !G && !U && !I )

3. Boys with no ID badge. ( !G || !I ) / ( !G && I ) / ( !G && !I )

Match the descriptions to the Venn diagrams by writing the number of the description in the blank above the diagram.

4. Girls who have ID, and their shirts are tucked-in 5. People with ID and un-tucked shirts 6. Boys who have un-tucked shirts and IDs 7. Girls who have neither IDs, nor un-tucked shirts 8. Girls who have IDs 9. Boys who have either IDs or un-tucked shirts 10. Girls who have either ID or un-tucked shirts 11. Girls who don’t have ID, but they do have un-tucked shirts 12. Girls who have ID and un-tucked shirts

_ _12 _ _ _5 _ _ _4 _ _ _8 _ _ _10_ _ _ _ 6 _ _ _7_ _

_ 17_ _ _ _15 _ _ 16_ _ _ _19 _ _ 13_ _ _ 14_ _ _ 18_ _ Match the logic expressions below with the Venn diagrams above by writing the number of the expression in the blank below the diagram.

13. G && ( I || U ) 14. !G && ( I && U ) 15. ( I && U ) 16. G && ( I && ! U )

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17. G && ( I && U ) 18. G && ( ! I && ! U ) 19. G && I

boolean a = false, b = false, c = true; if ( !a ){ System.out.print(a); a = !b; } if (!b && a){ c = !a; System.out.print(!c); } if (a || !c) { b = !b; System.out.print(b); }

20. When the code above runs, it will print [ truetruetrue / truefalsetrue / truetruefalse / falsefalsefalse / falsetruefalse / falsetruetrue

21. When the code above finishes running, the value of a is [ true / false ]

22. When the code above finishes running, the value of b is [ true / false ]

23. When the code above finishes running, the value of c is [ true / false ]

Complete the truth tables below. A B !A && !B True True False True False False False True False False False True A B !A || !B True True False True False True False True True False False True A B A || ! B True True True True False True False True False False False True

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Name: _________________________ Date: ____________________ Period: _____

Gates and Boolean Expressions Objective- Construct simple schematics from Boolean expressions, and translate schematics into Boolean expressions. Apply understanding of gates to create a schematic that satisfies output requirements. Instructions- Refer to the powepoint ‘Digital Gates’, if needed, to complete the exercise below. #1 Gates to Boolean Expressions

1. Write the Boolean expression for the following schematic.

Answer:

2. Write the Boolean expression for the following schematic.

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Answer: #2 Boolean Expressions to Gates

3. Draw the schematic for the Boolean expression !(A || B) && (!A && !B) #3 Problem Solving- Design a circuit that receives binary numbers as input, and turns on certain lights, depending on the input. There are only two inputs ( A, B) on which four different binary numbers may be represented. Remember that binary 00 = 0, binary 01 = 1, binary 10 = 2, binary 11 = 3. The circuit has three outputs ( #1, #2, #3). Each output is attached to a light. If there are 5 volts on the output, the light is turned on. If no lights are on, this represents zero. If the light on output #1 is on, it represents “one”, if light #2 is on, it represents a “two”, if light #3 is on it represents a “three”. Make sure that the circuit behaves according to the table below. The 0’s and 5’s in the input and output rows represent 0 and 5 volts. Use scratch paper to work through the problem and copy a working circuit to the space below. Hint- consider the inputs for each output separately. Counting Number

0 1 2 3

Input A 0 5 0 5 Input B 0 0 5 5 Output #1 0 5 0 0

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Output #2 0 0 5 0 Output #3 0 0 0 5

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Name: _________________________ Date: ____________________ Period: _____

Gates and Boolean Expressions KEY Objective: Construct simple schematics from Boolean expressions, and translate schematics into Boolean expressions. Apply understanding of gates to create a schematic that satisfies output requirements. Instructions: Refer to the Presentation ‘Digital Gates,’ if needed, to complete the exercise below. #1 Gates to Boolean Expressions

1. Write the Boolean expression for the following schematic.

KEY: !((( !A &&B) || !C) || (!A &&B))

2. Write the Boolean expression for the following schematic.

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KEY: !(!A && B) && (A || !B) #2 Boolean Expressions to Gates

3. Draw the schematic for the Boolean expression !(A || B) && (!A && !B)

#3 Problem Solving: Design a circuit that receives binary numbers as input, and turns on certain lights, depending on the input. There are only two inputs: ( A, B) on which four different binary numbers may be represented. Remember that binary 00 = 0, binary 01 = 1, binary 10 = 2, and binary 11 = 3. The circuit has three outputs (#1, #2, #3). Each output is attached to a light. If there are 5 volts on the output, the light is turned on. If no lights are on, this represents zero. If the light on output #1 is on, it represents “one;” if light #2 is on, it represents a “two;” if light #3 is on it represents a “three.” Make sure that the circuit behaves according to the table below. The 0’s and 5’s in the input and output rows represent 0 and 5 volts. Use scratch paper to work through the problem and copy a working circuit to the space below. Hint: consider the inputs for each output separately. Counting Number

0 1 2 3

Input A 0 5 0 5 Input B 0 0 5 5 Output #1 0 5 0 0 Output #2 0 0 5 0 Output #3 0 0 0 5 KEY- The simplest circuit is three AND gates. The first AND gate has inputs A && !B, the second AND gate has inputs !A && B, the third AND gate has inputs A&&B.