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
1
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
2
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: <>
3
Samples
4
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
5
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
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Evaluating Boolean Expressions to
Make Comparisons
• Dual-alternative (or binary) selection
structure:
– Provides an action for each of two possible
outcomes
7
Evaluating Boolean Expressions to
Make Comparisons (continued)
• Dual-alternative (or binary) selection
structure:
– Also called an if-then-else structure
8
Dual Alternative
If something is true Then
Do something
Else
Do something else
End If
If Age >= 18 Then
Set Eligibility = ‘Yes’
Else
Set Eligibility = ‘No’
End If
9
Using the Relational Comparison
Operators
Each calculates a discount of 10% only when the customer age is 65 years old or greater
IF customerAge >= 65 THEN
discount = 0.10
ELSE
discount = 0
ENDIF
IF customerAge < 65 THEN
discount = 0
ELSE
discount = 0.10
ENDIF
IF customerAge < 64 THEN
discount = 0
ELSE
discount = 0.10
ENDIF
ALL ARE CORRECT – THERE ARE NO WRONG WAYS!
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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.
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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
12
Evaluating Boolean Expressions to
Make Comparisons
• Single-alternative (or unary) selection
structure
– Action is provided for only one outcome
13
Evaluating Boolean Expressions to
Make Comparisons (continued)
• Single-alternative (or unary) selection
structure
– Also called an if-then structure
14
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
15
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.
16
More Examples
Given: A = 23, B = 16
Then:
A
A
A
A
A
A
> B is true
< B is false
>= B is true
<= B is false
<> B is true
= B is false
17
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.
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The Assignment Operator
Given: A = 14, B = 27
In 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.
19
The Comparison Operator
Given: A = 14, B = 27
Using the relational operators, the statement:
A == B
is 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.
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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”
“boy” > “apple”
“abc” <> “a b c”
“String” <> “string”
21
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.
22
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
23
Understanding AND Logic
• AND decision
– Requires that both (ALL) of two tests evaluate to
True
– Requires a nested decision (nested if)
24
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.
25
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
26
27
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
28
29
Avoiding Common Errors in an OR
Selection
• Incorrect interpretation of English
– Use of OR when AND logic is required > 12: All patrons (including 65 and above)
< 65: All patrons (including 12 and below)
30
Avoiding Common Errors in an OR Selection
• Correct logic:
31
• How many decisions?
32
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’.
33
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
34
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)
35
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
36
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 …
37
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.
38
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
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Hierarchy of Operations
Type
Operator
Order Performed
Arithmetic
operations
( )
^
* / %
+ -
1st parentheses
2nd exponentiation
3rd: multiplication,
division, modulus
4th: addition,
subtraction
are performed first, in
order shown
Relational
operations
are performed second
Logical operations
are performed last, in
the order shown
= <>
<= >
NOT
AND
OR
<
>=
All relational operators
have equal
precedence
1st: NOT
2nd: AND
3rd: OR
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3.3 Selecting from
Several Alternatives
• Sometimes, we must handle more than
two options in a program.
If something is true Then
Do something
Else
If something else is true Then
Do something else
Else
Do a different something else
End If
End If
41
Example
If Age >= 18 Then
Set Eligibility = “Yes”
Else
If Age > 15 Then
Set Eligibility = “Maybe”
Else
Set Eligibility = “No”
End If
End If
42
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.
43
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 >
44
Range Selection
Task: print if empRate is 10 or 11
45
Range Selection
SYNTAX error
Good
46
Using Selections Within Ranges
• Using high-end values in the range check:
47
Using Selections Within Ranges
• Using low-end values in the range check:
48
Common Errors Using Range Checks
Unnecessary
Unnecessary
49
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
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
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.
52
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
53
Understanding the Case Structure
54
Understanding the Case Structure
55
Example
Select Case of Choice
Case: 1
Set Operation
Case: 2
Set Operation
Case: 3
Set Operation
Case: 4
Set Operation
End Case
= “Add”
= “Subtract”
= “Multiply”
= “Divide”
56
Another Example
• The Case statement can be used to compare any
combination of numbers, strings, characters, or variables
For example:
Input Entry
Select Case of Entry
Case: 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
57
• 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
58
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 Cost
If Cost <= 0 Then
Write “Invalid cost”
Else
Write “The cost is ”, Cost
End If
59
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.
60
Pseudocode Language (Ch 3)
In this chapter we added logical operators and selection.
Input
Input Variable
Assignment
Set Variable = 10
Output
Arithmetic Operations
Write “literal text”, Variable
( ) ^ * / %
Relational Operators
= <> < > >= <=
Selection
If condition Then
do something
Else
do something else
End If
+ -
Logical Operators
AND
OR
NOT
Select Case of something
Case: X
do something
Case: Y
do something
Default:
do something
End Case
61