3/5/2019 - universiti teknologi malaysia

3/5/2019

1

CHAPTER 5:

ARITHMETIC EXPRESSIONS

1

2

In this chapter, you will learn:

• The built-in operator for specific mathematical

or logical manipulations.

• The evaluation of operators in arithmetic

expressions in a precise sequence determined

by the rules of operator precedence

• The expressions using the mathematical

operators.

• Some C mathematical operations functions in

the standard library.

Chapter 5 Objectives

3

5.1 Introduction

5.2 Operators in C

5.3 Mathematical Expressions

5.4 Data Type Conversion

5.5 Mathematical Library Function

5.6 Summary

Chapter 5 Contents

4

Chapter 5 5.1 Introduction

• In mathematics, an expression (or mathematical expression)

is a finite combination of symbols that is well-formed

according to rules that depend on the context.

• Mathematical symbols can assign numbers (constants),

variables, operations, functions, punctuation, grouping, and

other aspects of logical syntax.

• Mathematical expressions include arithmetic expressions

that express that results in a numeric values: integer and

floating point numbers.

• The simplest arithmetic expressions are literals number and

variables.

3/5/2019

2

5

Chapter 5 5.1 Introduction

• Most C programs perform calculations using the C arithmetic

operators

• Note: the use of various special symbols not used in algebra.

_____________________________________________________________________________________________________________________________________

I Deitel, H.M. and Deitel, P.J (2013). C How to Program 7/E. United State of America: Pearson Education.

6

5.1 Introduction

5.2 Operators in C

• Operators precedence

• Sample algebraic and C expression




5.6 Summary

Chapter 5 Contents

7

Chapter 5 5.2 Operators in C

• An operator is a symbol that tells the compiler to perform

specific mathematical or logical manipulations.

• Used to perform operations on data.

• C language is rich in built-in operators and provides the

following types of operators:

• Arithmetic operators

• Assignment operators

• Relational operators

• Equality operators

• Logical operators

• Increment / Decrement operators

• Bitwise operators

8

• Few symbols in assignment statements which have been

used in programs.

• Assume, int a = 4, b = 5, d;

C Operation Arithmetic

Operator C Expression

Value of d after

assignment

Addition

+

d = a + b

9

Substraction

-

d = b - 2

3

Multiplication

*

d = a * b

20

Division

/

d = a/2

2

Modulus

%

d = b%3

2


Arithmetic operators

3/5/2019

3

9


• Assume, int x = 4, y = 5, z = 8;

Assignment

Operator

Sample

Expression

Similar

Expression

Value of variable

after assignment

+=

x += 5

x = x + 5

x = 9

-=

y -= x

y = y - x

y = 1

*=

x *= z

x = x * z

x = 32

/=

z /=2

z = z / 2

z = 4

%=

y %=x

y = y % x

y = 1

Assignment operators

10

• Assume, int y = 6, x = 5;

Relational Operators

Sample Expression

Value

>

y > x

T

<

y < 2

F

>=

x >= 3

T

<=

y <= x

F

Equality Operators

Sample Expression

Value

==

x == 5

T

! =

y ! = 6

F


Relational and Equality operators

11

Assume,

int x = 50;

Logical Operators Called Sample Operation

&&

AND

expression1 && expression 2

||

OR

expression1 || expression2

!

NOT

! expression

Expression !Expression Sample Expression

F

T

!(x == 60)

T

F

!(x != 60)


Logical operators

12


• Example: Assume, int x = 4, y = 5, z = 8;

T

T

T

(z >= y) && (x != 3)

Expression1 Expression2 Expression1 &&

Expression2 Sample Expression

F

F

F

(y > 10) && (z <= x)

F

T

F

(z <= y) && (x == 4)

T

F

F

(y != z) && (z < x)

3/5/2019

4

13


Increment / Decrement operators

Operator

Called

Sample

Expression

Similar

Expression

Explanation

++

preincrement

++a

a = a +1

a += 1

Increment a by 1, then use

the new value of a in

expression in which a

reside

++

postincrement

a++

a = a +1

a += 1

Use the current value of a

in the expression which a

reside, then increment a by

1

--

predecrement

--a

a = a -1

a -= 1

Decrement a by 1, then

use the new value of a in

expression in which a

reside

--

postdecrement

a--

a = a -1

a -= 1

Use the current value of a

in the expression which a

reside, then decrement a

by 1

14


Operators precedence

_____________________________________________________________________________________________________________________________________

I Deitel, H.M. and Deitel, P.J (2013). C How to Program 7/E. United State of America: Pearson Education. (pp.52)

• Parentheses are used in C expressions in the same

manner as in algebraic expressions.

• For example, to multiply a times the quantity b + c,

we write a * ( b + c ).

• C applies the operators in arithmetic expressions in a

precise sequence determined by the rules of operator

precedence, which are generally the same as those in

algebra.

15


_____________________________________________________________________________________________________________________________________


• The rules of operator precedence specify the order C uses

to evaluate expressions from left to right. • Summarized rules of operator precedence for the operators:

16

Operators

Associative

( )

Left to right

++ -- + - !

Right to left

* / %

Left to right

+ -

Left to right

< <= > >=

Left to right

= = !=

Left to right

&&

Left to right

| |

Left to right

= *= += - =

/= %=

Right to left


3/5/2019

5

17


_____________________________________________________________________________________________________________________________________


• Example : Evaluation of the operator precedence rules

y = a * x * x + b * x + c;

• The circled numbers under the statement indicate the order

in which C performs the operations

• Suppose variables a, b, c and x in the preceding second-

degree polynomial are initialized as follows: a = 2 b = 3 c = 7 x = 5

18


_____________________________________________________________________________________________________________________________________


19

Example 1:

int a=10, b=20, c=15, d=8;

a*b/(-c*31%13)*d

1. a*b/(-15*31%13)*d

2. a*b/(-465%13)*d

3. a*b/(-10)*d

4. 200/(-10)*d

5. -20*d

6. -160


Example 2:

int a=15, b=6, c=5, d=4;

d *= ++b – a/3 + c

1. d *= ++b – a/3+ c

2. d*=7- a/3+c

3. d*=7- 5+c

4. d*=2 + c

5. d*= 7

6. d = d*7

7. d = 28

21

Grouping with Parentheses

3/5/2019

6

22

example Given the declaration,

int a = 9, b = 2, c = 6, d = 10;

and the statement,

a * b / c + 4 > d != 3 * c % a;

Solve the above statement based on the operator

precedence. Show your steps.

SOLUTION: step operator

0 9 * 2/6+4>10 != 3 * 6 % 9

1 * 18 /6+4>10 != 3 * 6 % 9

2 / 3 +4>10 != 3 * 6 % 9

3 * 3 +4>10 != 18 % 9

4 % 3 +4>10 != 0

5 + 7 >10 != 0

6 > 0 != 0

7 != 0 23


Sample algebraic and C Expressions

_____________________________________________________________________________________________________________________________________


• Example: The following expression calculates the arithmetic

mean (average) of five terms.

• The parentheses are required to group the additions

because division has higher precedence than addition. • The entire quantity ( a + b + c + d + e ) should be

divided by 5.

• If the parentheses are erroneously omitted, we obtain a + b + c + d + e / 5, which evaluates incorrectly

as:

24


_____________________________________________________________________________________________________________________________________


• Example: The following expression is the equation of a

straight line:

• No parentheses are required because the multiplication

evaluated first as its precedence higher than addition.

25

Chapter 5

Write the formula in C statement.

a) .

b) .

c) .

Activity 5.3:

5.2 Operators in C

a+ b

c+ d

1

1+ x2

b2 - 4ac

3/5/2019

7

26

a) (b*b)-(4*a*c)

b) (a+b)/(c+d)

c) 1/(1+(x*x))

Solution 5.3:


27

5.1 Introduction

5.2 Operators in C


• Introduction

• Multiple assignment

• Combined assignment



5.6 Summary

Chapter 5 Contents

28

• We can create complex expressions using multiple

mathematical operators.

• An expression can be a literal, a variable, or a mathematical

combination of constants and variables.

• Mathematical expression can be used in assignment, printf, other statements:

• Examples:

Chapter 5 5.3 Mathematical Expressions

Introduction

area = 2 * PI * radius;

printf (“Border is: %d", 2*(l+w));

29


• Some types of mathematical expressions:

Expressions

Primary Binary Assignment Postfix Prefix

3/5/2019

8

30


Primary expression

31


Binary expression

32


Assignment expression

33


Prefix expression

3/5/2019

9

34


Postfix expression

35

• The ‘=‘ can be used to assign a value to multiple variables:

x = y = z = 5;

• Value of ‘=‘ is the value that is assigned.

• Associates right to left: x = (y = (z = 5));


Multiple assignment

Value is 5

36

• Look at the following statement:

sum = sum + 1;

• This will adds 1 to the variable sum.

• Examples:


37

• The combined assignment operators provide a shorthand for

these types of statements.

• The statement: sum = sum + 1;

is equivalent to sum += 1;


Combined assignment

Table: Combined assignment operators

3/5/2019

10

38


• For increment and decrement operators: ++, --

• Instead of a = a + 1 you can write a++ or ++a

• Instead of a = a - 1 you can write a-- or --a

• What is the difference?

num = 10;

ans = num++;

Post-increment Pre-increment

num = 10;

ans = ++num;

First assign num to ans,

then increment num.

In the end, num is 11

ans is 10

First increment num,

then assign num to ans.

In the end, num is 11

ans is 11 39

5.1 Introduction

5.2 Operators in C



• Type casting

• Named constant


5.6 Summary

Chapter 5 Contents

40

• Operations are performed between operands of the same type.

• If not of the same type, C will convert one to be the type of the

other.

• The type of the result depends on the types of the operands.

• If the types of the operands differ (e.g. an integer added to a

floating point number), one is "promoted" to other.

o The "smaller" type is promoted to the "larger" one. char int float double

• This can impact the results of calculations.

Chapter 5 5.4 Data Type Conversion

41


int and double

• If all operands are integer, the output will be integer,

otherwise, the output will be double

• Example:

//Program_05.c

main() {

int x = 3, y = 2, output1, output2;

double d = 2.0, output3, output4;

output1 = x / y;

output2 = x / d;

output3 = x / y;

output4 = x / d; }

3/5/2019

11

42

• Used for manual data type conversion

• Useful for floating point division using int

• Format:

(data type)variable


Type Casting

43

• Example 1: Get the remainder value


_____________________________________________________________________________________________________________________________________

Program_06.c: Compiled with Xcode, Apple Machine

int main( void )

{

double x = 3.0, y = 2.0, output;

output = x % y; // syntax error!!!

printf( "\n Output = %f\n\n", output);

}

44

• Solution 1:


_____________________________________________________________________________________________________________________________________


int main( void )

{

double x = 3.0, y = 2.0, output;

output = (int)x % (int)y; // free error

printf( "\n Output = %f\n\n", output);

}

45

• Example 2: Display the average marks


_____________________________________________________________________________________________________________________________________


int main( void )

{

int total_marks = 456, num_studs = 5;

double ave_marks1, ave_marks2;

ave_marks1 = total_marks/num_studs;

ave_marks2 = total_marks / num_studs;

printf( "\n ave_marks1 = %f\n\n", ave_marks1);

printf( " ave_marks2 = %f\n\n", ave_marks2);

}

Incorrect result !!!

3/5/2019

12

46

• Solution 2:


_____________________________________________________________________________________________________________________________________


int main( void )

{

int total_marks = 456, num_studs = 5;

double ave_marks1, ave_marks2;

ave_marks1 = total_marks/num_studs;

ave_marks2 = (double) total_marks / num_studs;

printf( "\n ave_marks1 = %f\n\n", ave_marks1);

printf( " ave_marks2 = %f\n\n", ave_marks2);

}

47

• Named constant (constant variable): variable whose content

cannot be changed during program execution.

• Used for representing constant values with descriptive names:

• Often named in uppercase letters


Named constant

const double TAX_RATE = 0.0675;

const int NUM_STATES = 50;

48

void main()

{

const int num = 5;

num++; // num=num+1

printf(“Value of new num is %d”, num);

}


• Example: What will be the output?

• Output:

49


#define

• Interpreted by pre-processor rather than compiler

• Does not occupy memory location like const

• Example: Increase the NUM value

#define NUM 5 //no semicolon (;)at end

void main()

{

NUM++; // Error: expression is not

assignable

printf(“Value of new NUM is %d”, NUM);

}

3/5/2019

13

50


• Solution: Declare a variable and write an assignment for it.

#define NUM 5

void main()

{

int new;

new = NUM + 1;

printf(“Value of NUM is %d”, new);

}

Value of new NUM is 6

• Output:

51

Chapter 5

Write a program that will convert Malaysian Ringgit

(RM) amounts to Japanese Yen. The conversion

factors to use are:

1 RM = 25.69218 Yen

Solve the problems using constant values.

Display the output as below:

Activity 5.4:


Tips: .

Refer

Program_04.c

Comment in your

program and save

your file as

Activity_5.4.c

53

5.1 Introduction

5.2 Operators in C




5.6 Summary

Chapter 5 Contents

54

Chapter 5 5.5 Mathematical Library Functions

• C mathematical operations are a group of functions in the

standard library of the C programming language implementing

basic mathematical functions.

• The library can be called upon during pre-processing #include

#include <math.h>

#include <stdlib.h>

• The math.h header defines various mathematical functions

and one macro.

• All the functions available in this library take double as an

argument and return double as the result.

3/5/2019

14

55

Chapter 5 5.5 Mathematical Library Functions

Function Library

Function

Example Argument Output

abs(x) stdlib.h x abs(-5)

output 5

int int

exp(x) math.h ex exp(1.0)

output 2.71828

double double

log(x) math.h loge(x) log((2.71828)

output 1.0

double double

pow(x, y) math.h xy

pow(0.16, 0.5)

output 0.4

double,

double

double

sqrt(x) math.h √x and x>=0.0 sqrt(2.25)

output 1.5

double double

Table: Some functions from mathematical library.

56

Chapter 5

Rewrite the following mathematical expressions using

C functions. Assume all variables should be of type

double.

a) .

b) log10(xy)

c) .

Activity 5.5:

5.5 Mathematical Library Functions

_____________________________________________________________________________________________________________________________________

I Hanly, J.R and Koffman, E.B. (2001). C Program Design for Engineers 2/E. United State of America: Addison Wesley Longman Inc. (pg: 100)

u+v ´w2

(x+ v)2

58

5.1 Introduction

5.2 Operators in C




5.6 Summary

Chapter 5 Contents

59

Chapter 5 5.6 Summary

• Computation of the data need a specific mathematical

or logical manipulations.

• The arithmetic expressions is operated in a precise

sequence determined by the rules of operator

precedence

• The arithmetic expressions may have multiple and

combined assignment operators.

• Some mathematical operations can be called using in

the standard library function provided in C.

3/5/2019

15

60

Self-Review

Chapter 5

61

Chapter 5

Given the declaration,

int a = 9, b = 2, c = 6, d = 10;

and the statement,

a * b / c + 4 > d != 3 * ++c >= a;

Solve the above statement based on the operator

precedence. Show your steps.

Activity 5.1:

5.2 Operators in C

63

Chapter 5

Given the declaration, int count = 5, x, y, c, d;

and the following statement: d = (x = 5, y = 10, c = (x * --count - y++));

What will be printed by the printf statement below?

printf ("%d %d %d %d", count, c, y, d);

Activity 5.2:

5.2 Operators in C

65

Chapter 5 Self-Review

Write a C program to calculate and display the power (watts) and

the current (amps) by obtaining an input of voltage from user.

Assume the resistance remain constant at 5 ohms.

Exercise 5.1:

3/5/2019 - universiti teknologi malaysia

Documents