1

Boolean Expressions to Make Comparisons

• Boolean expression– Represents only one of two states– Expression evaluates to either true or false

• Expressions with relational operators produce Boolean results:– hours worked > 40

2

Using the Relational Comparison Operators

• Six possible ways to compare two values:– Both are equal– The first is greater than the second– The first is less than the second– The first is greater than or equal to the second– The first is less than or equal to the second– The two values are not equal

3

Relational Comparison Operators

• Relational comparison operators:– To express Boolean tests when comparing values

• Different languages use different symbols – Equals: =– Less than: <– Greater than: >– Less than or equal: <=– Greater than or equal: >=– Not equal: <>

4

Samples

5

Relational Comparison Operators

• Any logical situation can be expressed with only three types of comparisons: =, >, and <

• >= and <= are not necessary, but make code more readable

• Adjust the logic based on the comparison type

6

3.1 An Introduction to Selection Structures

• Single-alternative (If-Then)– A single block of statements to be executed or

skipped

• Dual-alternative (If-Then-Else )– Two blocks of statements, one of which is to be

executed, while the other one is to be skipped

• Multiple-alternative – More than two blocks of statements, only one of

which is to be executed and the rest skipped

7

Evaluating Boolean Expressions to Make Comparisons

• Dual-alternative (or binary) selection structure:– Provides an action for each of two possible

outcomes

8

Evaluating Boolean Expressions to Make Comparisons (continued)

• Dual-alternative (or binary) selection structure:– Also called an if-then-else structure

9

Dual Alternative

If something is true ThenDo something

ElseDo something else

End If

If Age >= 18 ThenSet Eligibility = ‘Yes’

ElseSet Eligibility = ‘No’

End If

10

IF customerAge >= 65 THEN discount = 0.10ELSE discount = 0ENDIF

IF customerAge < 65 THEN discount = 0ELSE discount = 0.10ENDIF

IF customerAge < 64 THEN discount = 0ELSE discount = 0.10ENDIF

Using the Relational Comparison Operators

Each calculates a discount of 10% only when the customer age is 65 years old or greater

ALL ARE CORRECT – THERE ARE NO WRONG WAYS!

11

Guidelines

• An Else condition does not have to exist. Sometimes we only want to do something if something is true and do nothing if it is not true.

• Do not manufacture alternative conditions.

• Be sure to indent for readability.

• Do not use the word Then after an Else.

12

Single Alternative

If something is true Then Do something (any number of statements)End If

If Age >= 18 Then

Set Eligibility = “Yes”

Do other things…

End If

13

Evaluating Boolean Expressions to Make Comparisons

• Single-alternative (or unary) selection structure– Action is provided for only one outcome

14

Evaluating Boolean Expressions to Make Comparisons (continued)

• Single-alternative (or unary) selection structure– Also called an if-then structure

15

Relational Operators

• Relational operators are the symbols used in the condition to be evaluated in If statements:

= equal to

<> not equal to

< less than

> greater than

<= less than or equal to

>= greater than or equal to

16

Example

• The If statement:If A > B Then Write A ,”is greater than”, B

End If

• Can be read: If it is true that the value of the variable A is greater than the value of the variable B, then write “A is greater than B” to the screen.

17

More Examples

Given: A = 23, B = 16

Then:A > B is true

A < B is false

A >= B is true

A <= B is false

A <> B is true

A = B is false

18

Comparison vs. Assignment Operators

The equals sign (=) in this text may have two different meanings. The difference is very significant.

As an assignment operator, the equals sign sets the value of an expression on the right side to the variable on the left side.

As a comparison operator, the equals sign asks the question, “Is the value of the variable on the left side the same as the value of the expression, number, or variable on the right side?”

Many programming languages distinguish between these two operators as follows:

• a single equals sign (=) signifies the assignment operator

• a double equals sign (==) signifies the comparison operator

This is demonstrated in the examples that follow in the next slides.

19

The Assignment Operator

Given: A = 14, B = 27In programming code, the assignment

statement:A = B

sets the value of B to the variable A. In other words, after this statement is executed, both A = 17 and B = 17. In this case, the equals sign is used as an assignment operator.

20

The Comparison Operator

Given: A = 14, B = 27Using the relational operators, the statement:

A == Bis a comparison. This statement asks the question, “Is the

value of A the same as the value of B?” In this case, since A and B have different values, the answer is “no” and the statement would result in a value of False.

In this text, we often use the one symbol (=) to represent both assignment and comparison operators and rely on the context to make the meaning clear.

21

Using Relational Operators on Strings

• Two strings are equal if they contain exactly the same characters in the same order. Otherwise they are not equal.

• If two strings consist of letters, alphabetical order determines the effect of the operators.

• Examples: “a” < “b” “abc” <> “a b c”“boy” > “apple” “String” <> “string”

22

Logical Operators

• Logical operators are used to connect simple conditions into a more complex condition called a compound condition.

• The simple conditions each contain one relational operator.

• Using compound conditions reduces the amount of code that must be written.

23

Combining Decisions in an AND Selection

• Logical AND operator: – Allows you to ask two or more questions

(Boolean expressions) in a single comparison– Each Boolean expression in an AND selection

must be true to produce a result of true– Question placed first will be asked first, so

consider efficiency

24

Understanding AND Logic• AND decision

– Requires that both (ALL) of two tests evaluate to True

– Requires a nested decision (nested if)

25

The AND Operator• A compound condition consisting of two

simple conditions joined by an AND is true only if both simple conditions are true. It is false if even one of the conditions is false. The statement: If (X > 5) AND (X < 10) Then …

is true only if X is 6, 7, 8, or 9. It has to be both greater than 5 and less than 10 at the same time.

26

Writing Nested AND Decisions for Efficiency (continued)

• Rule of Thumb: First ask the question that is less likely to be true – more likely to be false (first false terminates the question)– Reduces the number of times the second question will need

to be asked

27

28

Understanding OR Logic• OR decision

– At least one of two conditions must be true to produced a result of True

– If first condition is true, no need to test the second condition

29

30

Avoiding Common Errors in an OR Selection

• Incorrect interpretation of English– Use of OR when AND logic is required

< 65: All patrons (including 12 and below)

> 12: All patrons (including 65 and above)

31

Avoiding Common Errors in an OR Selection

• Correct logic:

32

• How many decisions?

33

The OR Operator

• A compound condition consisting of two simple conditions joined by an OR is true if even one of the simple conditions is true. It is false only if both are false. For example:

If (Response =“Y”) OR (Response =“y”) Then …

• This is true if Response is uppercase or lower case y. For the above condition to be false, Response would have to be something other than either ‘Y’ or ‘y’.

34

Combining Decisions in an OR Selection

• Logical OR operator: – Allows you to ask two or more questions

(Boolean expressions) in a single comparison

– Only one Boolean expression in an OR selection must be true to produce a result of true

– Question placed first will be asked first, so consider efficiency

35

Writing OR Decisions for Efficiency

• Both produce the same output, but vary widely in number of questions asked

• If first question is true, no need to ask second

• Rule of thumb:– First ask the question that is more likely to be

true (first true will generate the TRUE path and the rest of the ORs will be ignored)

36

Example

This code is

equivalent to

Input X

If X < 5 Then

Write “OK”

End If

If X > 10 Then

Write “OK”

End If

this code. But this code is shorter!

Input X

If (X<5) OR (X>10) Then

Write “OK”

End If

37

Hints

• In a compound condition, it is necessary to use complete simple conditions.

• This is correct:If (X < 5) OR (X > 10) Then …

• This is not correct:

If (X < 5 OR > 10) Then …

38

The NOT Operator• AND and OR affect 2 simple conditions.• NOT affects only one condition. If you need to negate

more than one simple condition, you will need more than one NOT.

• A condition with the NOT operator is true only if the condition is false.

NOT ( A < B)

is true only if B is greater than or equal to A.If ( X > 100) AND NOT ( X = Y) Then…

is true only if X is greater than 100 but not equal to the value of Y.

39

Truth Tables for OR, AND, and NOT Operators

X Y X OR Y X AND Y NOT X

true true true true false

true false true false false

false true true false true

false false false false true

40

Hierarchy of OperationsType Operator Order Performed

Arithmetic operations

are performed first, in order shown

( )

^

* / %

+ -

1st parentheses

2nd exponentiation

3rd: multiplication, division, modulus

4th: addition, subtraction

Relational operations

are performed second

= <> < <= > >=

All relational operators have equal precedence

Logical operations

are performed last, in the order shown

NOT

AND

OR

1st: NOT

2nd: AND

3rd: OR

41

3.3 Selecting fromSeveral Alternatives

• Sometimes, we must handle more than two options in a program.

If something is true Then Do somethingElse

If something else is true ThenDo something else

ElseDo a different something

elseEnd If

End If

42

Example

If Age >= 18 ThenSet Eligibility = “Yes”

Else If Age > 15 Then

Set Eligibility = “Maybe”Else

Set Eligibility = “No”End If

End If

43

Hints

• The number of End If’s must equal the number of If’s.

• You can draw a line to connect them to check.

• In the previous example, the check for Age = 5 will never be done if the Age is > 18.

• Regardless of how many possible conditions are included, only one will ever be executed.

44

Using Selections Within Ranges

• Range check: compare a variable to a series of values between limits

• Use the lowest or highest value in each range• Adjust the question logic when using highest

versus lowest values• Should end points of the range be included?

– Yes: use >= or <=– No: use < or >

45

Range Selection

Task: print if empRate is 10 or 11

46

SYNTAX error

Range Selection

Good

47

Using Selections Within Ranges

• Using high-end values in the range check:

48

Using Selections Within Ranges• Using low-end values in the range check:

49

Common Errors Using Range Checks

Unnecessary

Unnecessary

50

Understanding Precedence When Combining AND and OR Selections

• When AND and OR operators are combined in the same statement, AND operators are evaluated first

• Use parentheses to correct logic and force evaluations to occur in the order desired

51

Understanding Precedence When Combining AND and OR Selections

• When AND and OR operators are combined in the same statement, AND operators are evaluated first

• Use parentheses to correct logic and force evaluations to occur in the order desired

52

Case-type Statements

• Case or Switch statements can be used to more easily code multiple alternative If’s

• Use the special or keyword Case.• Use Select to start the Case statement.• Specify the expression to be evaluated.• List each possible value of the expression and

what to do if that is that value is the true one.• Use End Case to end the statement• The results will be the same as a correctly coded

multiple-alternative If-Then-Else structure.

53

Understanding the Case Structure

• Used to provide a series of alternatives (IF statements) based on the value of a single variable

• Replaces a series of chained if-else statements

• May make the code easier to read

54

Understanding the Case Structure

55

Understanding the Case Structure

56

Example

Select Case of ChoiceCase: 1

Set Operation = “Add” Case: 2

Set Operation = “Subtract” Case: 3

Set Operation = “Multiply” Case: 4

Set Operation = “Divide”End Case

57

Another Example

• The Case statement can be used to compare any combination of numbers, strings, characters, or variables

For example:Input EntrySelect Case of EntryCase: Password

Write “Welcome!”Case: “new user”

Write “Click on New to open an account”Case: 0

Write “Goodbye”Default:

Write “Do not understand. Try again.”End Case

58

• AND decision requires that both conditions be true to produce a true result

• OR decision requires that either of the conditions be true to produce a true result

• Case structure allows a series of alternative actions based on the value in a single variable

59

Applications of Selection Structures

• Program defensively in order to prevent bad data from entering our program. To do this, set error traps (idiot proofing).

• If our program should accept only a Cost greater than 0, we can stop any other value from entering with the following trap:Input CostIf Cost <= 0 ThenWrite “Invalid cost”

Else Write “The cost is ”, Cost

End If

60

Defensive Programming

• Be sure to test your program by ‘playing computer.’ (Deskchecking)

• Perform all calculations multiple times manually• Use data that will show the results when each

branch of each selection structure is executed at least once.

• Check for division by zero, negative values, Nulls and other special conditions.

61

Pseudocode Language (Ch 3)In this chapter we added logical operators and selection.Input Assignment

Input Variable Set Variable = 10

Output Arithmetic Operations

Write “literal text”, Variable ( ) ^ * / % + -

Relational Operators Logical Operators

= <> < > >= <= AND OR NOT

Selection If condition Then Select Case of something do something Case: XElse do something do something else Case: YEnd If do something

Default:do something

End Case