Chapter 4

Arithmetic and Logical Expressions

BTE2313 Computer Programming

Lecturer: Samson Mekbib

LEARNING OUTCOME

Learn about arithmetic operators to preform calculations in C++

Explain how to solve and create a logical expression

Explain how to use operators AND ( && ) and OR ( l l )

LEARNING OUTCOME

Learn about arithmetic operators to preform calculations in C++

Explain how to solve and create a logical expression

Explain how to use operators AND ( && ) and OR ( l l )

Operator shortcuts

Example: Operator shortcuts

Logical relationship

To make decisions, you must be able to express conditions and make comparisons

Stating conditions and making comparisons

In C++ a condition is represented by a logical (Boolean) expression

True and False are logical (Boolean) values

RELATIONAL OPERATORS: A relational operator allows you to make comparison in a program

Relational operators:

Allow comparison

Require two operands

Evaluate to True or False

Relational operators in C++

N.B. : In C++, the symbol ==, which consists of two equal signs, is called the equivalence operator and determines whether two expressions are equal, whereas the assignment operator =, assigns the value of an expression to a variable.

Operator Description Example True when Value of num is

False when value of num is

== Equal to num == 10 10 Other than 10

!= Not equal to num != 10 Other than 10 10

> Bigger than num > 10 Bigger than 10 10 or smaller

>= Bigger than or equal num >= 10 10 or bigger Smaller than 10

< Less than num < 10 Smaller than 10 10 or bigger

<= Less than or equal num <= 10 10 or smaller Bigger than 10

! Not !(num==10) Other than 10 10

Relational operators and simple data types

You can use the relational operators with all the simple data types

Examples with integers and real numbers

Expression Meaning Value

8 < 15 8 is less than 15 true

6 != 6 6 is not equal to 6 false

2.5 > 5.8 2.5 is greater than 5.8 false

5.9 <= 7.5 5.9 is less than or equal to 7.5 true

Example: Equality of floating point numbers

Boolean Algebra

Or truth table

P Q P or Q

False False False

False True True

True False True

True True True

Boolean Algebra

Not truth table

P not P

False True

True False

Boolean Algebra

Can create complex logical expressions by combining simple logical expressions

Example

not (P and Q)

A truth table can be used to determine when a logical expression is true

P Q P and Q not (P and Q)

False False False True

False True False True

True False False True

True True True False

A Boolean Type C++ contains a data type named bool

Type bool data type has two symbolic constants

true

false

Examples

bool P = true;

bool Q = false;

bool R = true;

bool S = (P && Q);

The insertion and extraction operators could be used with bool types

In the output bool objects are displayed in binary notations (0 or 1)

Example:

cout << P << endl;

will print out either 1 or 0, depending on whether P is true or false respectively

A Boolean Type

Example: Suppose the following bool type objects are defined

bool P = true;

bool Q = false;

bool R = true;

bool S = false;

Then,

P is true Q

P && R P && S

P l l Q Q l l S

!S !R

true false

Logical (Boolean) Operators

Examples of logical expressions

Operator Precedence Revisited

Level Operator Associativity Type

1 () Left to right Parentheses

2 +, -, ++, --, ! Right to left Unary

3 *, /, % Left to right Multiplicative

4 +, - Left to right Additive

5 <<, >> Left to right Insertion/extraction

6 <, <=, >, >= Left to right Relational

7 ==, != Left to right Equality

8 && Left to right Logical AND

9 l l Right to left Logical OR

Operator Precedence Revisited

Example: Consider

5 * 15 + 4 == 13 && 12 < 19 || !false == 5 < 24

Is equivalent to:

((((5 *15) + 4) == 13) && (12 < 19))

||

((!false) == (5 < 24))

N.B. This is just an example and you will not be

using such complicated statements in your

programs.

Introductions on next chapter Conditional / Selection Structure

Examples: Simple conditional statements

if (score is greater than or equal to 90)

grate is A

if (hours worked are less than or equal to 40)

wages = rate * hours

Otherwise

wages = (rate * 40) + 1.5 * (rate * (hours -40))

if (temperature is greater than 20 degrees and it is not raining)

go to play golf!

Conditional Constructs in C++

Provide

Ability to control whether a statement list is executed

Two constructs

If statement

if

if-else

if-else-if

The Basic If Statement

Syntax

if (Expression)

Action

If the Expression is true then execute Action

Action is either a single statement or a group of statements within braces

Expression

Action

true false

Example

if (Value < 0) {

Value = -Value;

}

Value < 0

Value = -Value

true f alse

Is our number negative?

If Value is not less

than zero then our

number is fine as is

If Value is less than

zero then we need to

update its value to

that of its additive

inverse

Our number is

now definitely

nonnegative

Sorting Two Numbers

cout << "Enter two integers: ";

int Value1;

int Value2;

cin >> Value1 >> Value2;

if (Value1 > Value2) {

int RememberValue1 = Value1;

Value1 = Value2;

Value2 = RememberValue1;

}

cout << "The input in sorted order: "

<< Value1 << " " << Value2 << endl;

Semantics

value2 < value1

int rememberValue1 = value1

value1 = value2

value2 = rememberValue1

true f alse

Are the numbers

out of order

Rearrange value1

and value2 to

put their values

in the proper

order

The numbers were

initially in order

The numbers were

rearranged into the

proper order

The numbers are in

order

What is the Output?

int m = 5;

int n = 10;

if (m < n)

++m;

++n;

cout << " m = " << m << " n = " n << endl;

The If-Else Statement Syntax

if (Expression)

Action1

else

Action2

If Expression is true then execute Action1 otherwise execute Action2

if (v == 0) {

cout << "v is 0";

}

else {

cout << "v is not 0";

}

Expression

Action1 Action2

true false

Finding the Max

cout << "Enter two integers: ";

int Value1;

int Value2;

cin >> Value1 >> Value2;

int Max;

if (Value1 < Value2) {

Max = Value2;

}

else {

Max = Value1;

}

cout << "Maximum of inputs is: " << Max << endl;

Finding the Max

Value1 < Value2

Max = Value2 Max = Value1

true f alse

Is Value2 larger than Value1

Yes, it is . So Value2 is

larger than Value1. In

this case, Max is set

to Value2

No, its not. So Value1

is at least as large as

Value2. In this case,

Max is set to Value1

Either case, Max is set

correctly

Selection

It is often the case that depending upon the value of an expression we want to perform a particular action

Two major ways of accomplishing this choice

if-else-if statement

if-else statements “glued” together

Switch statement

An advanced construct

An If-Else-If Statement

if ( nbr < 0 )

{

cout << nbr << " is negative" << endl;

}

else if ( nbr > 0 )

{

cout << nbr << " is positive" << endl;

}

else

{

cout << nbr << " is zero" << endl;

}