OPERATORS AND EXPRESSIONS

 

CHAPTER – 2 : OPERATORS AND EXPRESSIONS

 

OPERATORS IN C

C has a rich set of operators. They may operate on a single operand or two operands. They are used to perform basic arithmetic operations, comparisons, manipulation of bits and so on. C operators are broadly classified into three main categories.

1] Unary Operators

2] Binary Operators

3] Ternary Operators

 

1] UNARY OPERATORS :

An operator that acts upon only one operand is known as a unary operator. The C unary operators are :

1)        Unary minus ( - )

2)        Logical NOT operator ( ! )

3)        Bitwise Complementation ( ~ )

 

2] BINARY OPERATORS :

These operators act upon two operands. Hence the name binary. The binary operators are further classified into 4 categories.

1)        Arithmetic Operators

2)        Relational Operators

3)        Logical Operators

4)        Bitwise Operators

 

3] TERNARY OPERATORS :

These operators act upon three operands. Hence it is called ternary operator. It is known as conditional operator.

 

TYPES OF OPERATORS :

 

1)        Arithmetic Operators

2)        Relational Operators

3)        Logical Operators

4)        Assignment Operators

5)        Increment and decrement Operators

6)        Conditional Operators

7)        Bitwise Operators

8)        Special Operators

 

1] ARITHMETIC OPERATORS :

Arithmetic operators are used to perform the basic arithmetic operations such as addition, substraction, multiplication and division. The modulus operator is added to the list of C arithmetic operators. It is used for finding the remainder after an integer division.

 

Operation	Operator	Precedence	Associatively
Addition	+	2	L to R
Substraction	-	2	L to R
Multiplication	*	1	L to R
Division	/	1	L to R
Modulus	%	1	L to R

Addition Operator ( + ) : This operator adds the two data values (operands) that appear on either side of it.

Example :       sum = num1+num2;

Substraction Operator ( - ) : The operand that appears to the right of the operator is substracted from the operand that is the left of it.

Example :       net = amount – discount;

Multiplication Operator ( * ) : The two operands that appear on either side of the operator are multiplied.

Example :       mul = a * b;

Division Operator ( / ) : The value to the left of / is divided by that on the right.

Example :       div = x / y;

Modulus Operator ( % ) : This operator evaluates the remainder of an integer division operation.

Example :       rem = x % y;

 

2] RELATIONAL OPERATORS :

 

These are used to compare two operands. They define the relationship existing between two constants or variables. They result in either a TRUE or FALSE value. The value of TRUE is nonzero (i.e, 1) and that of FALSE is zero.

 

Operator	Meaning	Precedence	Associativity
<	Lesser than	1	L to R
< =	Less than or equal to	1	L to R
>	Greater than	1	L to R
> =	Greater than or equal to	1	L to R
= =	Equal to	2	L to R
! =	Not equal to	2	L to R

Example :

If a =100, b=80 Then (a > b) is true

(a < b) is false

 

Difference between = and = = operator

 

= = operator		= operator
1.	= = is relational operator.	1. = is assignment operator.
2.	= = sign does not change the value of an identifier.	2.	= operator changes the value of the variable to its left.

 

3] LOGICAL OPERATORS :

 

These operators are used to take decisions. These are three such operators. They are AND, OR and NOT. The result of these operators is either TRUE or FALSE. The logical operators are  used to connect one or more relational expressions.

 

Operator	Meaning	Precedence	Associativity
&& (double ampersand)	Logical AND	2	L to R
|| (double pipeline)	Logical OR	3	L to R
! (exclamation)	Logical NOT	1	L to R

The logical AND operator is used to perform operation on two operands. It is equivalent to a multiplication operation. The result of a logical AND is true, when both the operands are true; otherwise the answer is false.

 

Operand1	Operand2	Operand1 && Operand2
False	False	False
False	True	False
True	False	False
True	True	True

 

The logical OR operator is used to perform operation on two operands. It is equivalent to a addition operation. The result of a logical AND is false, only when both the operands are false; otherwise the answer is true.

 

Operand1	Operand2	Operand1 && Operand2
False	False	False
False	True	True
True	False	True
True	True	True

 

The logical NOT is used to obtain the logical complement of the operand. The result of a logical NOT is TRUE when the operand is FALSE and vice-versa.

 

Operand	! Operand
False	True
True	False

 

Example : If i = 8, x = 5.1, c=’a’ Then

1.   ( i > 6 ) && ( c = = ‘a’ )                     is true or 1

2.   ( i <= 6 ) | | ( c = = ‘b’ )                      is false or 0

3.   ( i >= 6 ) && ( c = = ‘97’)                  is true

4.   ( x < 10 ) | | ( i > 10 )                          is true

 

4] ASSIGNMENT OPERATORS :

The assignment operator = is used to assign the value of a variable, constant or expression to a variable.

Syntax :

variable = variable / constant / expression ;

 

Example :

a = 10;

b = 10;

sum = a + b

 

C also provider abbreviated or short hand assignment operators.

Syntax :

Variable Operator = Expression;

 

Example :

n = n + 5; can be written using the short hand assignment

n + = 5;           where + = is the abbreviated or compound operator.

5] INCREMENT AND DECREMENT OPERATORS :

 

INCREMENT OPERATOR :

This operator is used to increment the value of an integer quantity by one. This is represented by ‘++’ (double plus) symbol. This symbol can be placed before or after the integer variable, then

++int_var          -      indicates pre increment i.e., the value of int_var must be incremented before it is used. (increment and use)

int_var++     - indicates post increment i.e., the value of  int_var is used first then increment it (use and increment)

 

Example :        int x, y; x = 10;

y = ++ x;

 

DECREMENT OPERATOR :

This operator is used to reduce the value of an integer quantity by one. This is represented by ‘--’ (double minus) symbol. This symbol can be placed before or after the integer variable, then

--int_var       -    indicates decrement the value of int_var first and then use it.

int_var--       - indicates use the value of int_var first and then decrement it.

 

Example : int x, y; x = 10;

y = -- x;

 

Difference between post fix and pre fix operators :

Pre-increment/decrement	Post increment/decrement
1. The pre increment or decrement operator first increment or decrement the value of its operand by 1 and then assigns the resulting value to the variable on the left hand side. For example : int a, b; a = 15;     b = + + a; Here, the value of a is incremented by 1 and then this value 16 is assigned to b.	2. The post increment or decrement  operator first assigns the value to the variable on the left hand side and then increment or decrements the operand by 1. For example : int m, n; n = 2; m = n - - ; Here, the value of n is first assigned to m  and then decremented by 1, i.e., n becomes 1, but value of m is 2.

 

6] CONDITIONAL OPERATOR ( TERNARY OPERATOR) :

The ternary operator is a conditional operator in C. There is only one such operator in C. It takes three operands. The symbol ‘?’ is used as a ternary operator in C.

Syntax :

Variable = expr1 ? expr2 : expr3 ; The general form of ternary expression is :

Variable = (condition) ? true : false ;

 

1.         The expr1 is evaluated first.

2.         If expr1 is true, expr2 is evaluated and its value assigned to variable.

3.         If expr1 is false, expr3 is evaluated and its value assigned to the variable.

4.         Either expr2 or expr3 will be evaluated, but never both.

Example :       m = 5; n = 10;

big = ( m > n ) ? m : n ;

 

In the above example m > n is evaluated first giving the result false. Since the expr1 is false the value of n is assigned to big. Therefore the value of big is 10.

 

7] BITWISE OPERATORS :

All data items are stored in the computer’s memory as a sequence of bits (0’s and 1’s), and some applications need the manipulation of these bits. Manipulation of individual bits is carried out in machine language or assembly language. To perform, the bitwise operations, C provides six operators. These operators work with int and char type data. They cannot be used with floating-point numbers.

 

Operators	Symbol Name	Meaning
&	Ampersand	Bitwise AND
|	Pipeline	Bitwise OR
^	Caret	Exclusive – OR (XOR)
~	Tilde	1’s complement
<<	Double less than	Left shifting of bits
>>	Double greater than	Right shifting of bits

 

Note : Bitwise operators cannot be applied to float or double. They can be applied to integers only.

 

Bitwise AND operator : It is represented by the symbol & (ampersand). The result of AND operation is 1 if both operand bits are 1, otherwise, the result is zero.

Example :       x=4 & y=5 results in 4

i.e., binary value of x is 0100 binary value of y is 0101

-----------

x & y,  After AND operation    0100      i.e., 4

 

Bitwise OR operator : It is represented by the symbol | (pipe). It is also known as Inclusive OR. The result of bitwise OR operation is 1 if either or both corresponding bits has a value 1, otherwise it is zero.

Example : x = 4 and y = 9

i.e., binary value of x is 0100 binary value of y is 1001

-----------

x | y,    After OR operation is    1101     i.e., 13

 

Bitwise exclusive OR operator : It is represented by the symbol ^ (caret). The result of bitwise exclusive OR operation is 1, if one of the corresponding bit is 1, otherwise it is zero.

Example :       x = 4 and y = 9

i.e., binary value of x is 0100 binary value of y is 1001

-----------

x ^ y, After exclusive OR operation is 1101     i.e., 13

Bitwise Complement operator : The complement operator is represented by ~ (tilde) and is also known as one’s complement.

Example :       x = 4

i.e., x is 0100 Then

~x is 1011

 

Bitwise shift operator : The shift operators are used to push the bit patterns to the right or left by the bit number of bits given by their right operand.

 

The Right Shift operator is of the form :

Syntax :

Expression >> n;

Where n is the number of bit positions to be shifted. However, the right most n bits are lost.

Further the left most n bits which are vacant will be filled with 0. Example : num contains the bit pattern

110011110 then

Num>>1 gives 011001111

Num>>3 gives 000110011

Num>>5 gives 000001100

 

The Left Shift operator is of the form :

Syntax :

Expression << n,

Where n is the number of bit positions to be shifted. The leftmost n bits are lost and the right most n bits are vacant and filled with zeros.

Example :       num contains the bit pattern

11010111 then

Num<<1 gives 10101110

Num<<3 gives 10111000

Num<<5 gives 11100000

 

8] SPECIAL OPERATORS OF C

C contains the following special operators.

Operator	Description
,	Comma operator
sizeof	Size in bytes
&	Address of operand
*	Access value from the address
. (dot)	Dot operator
€	Arrow operator

 

COMMA OPERATOR :

The comma operator is basically associated with the for statement. It is also used to link two or more related expressions together. In such cases, the expressions are evaluated in a left-to-right fashion. And, we can obtain the value of the combined expression from the value of the rightmost expression.

Example: sum = (a = 12, b = 22, a+b);

There are three expressions namely, a = 12, b = 22 and a + b. The value of the rightmost expression, 33 (i.e., a + b = 12 + 22 = 33) is set to the variable sum.

sizeof( ) OPERATOR :

The sizeof( ) operator returns the size (i.e., number of bytes) of an operand. It is a function and therefore has to be written in lowercase letters. It must precede its operand. The operand may be constant, a variable or a data type. It is normally used to determine the size of arrays and structures. The syntax of sizeof( ) operator is as follows.

sizeof(operand);

 

Example :

x = sizeof(int); y = sizeof(sum);

 

Consider the following table :

Variable declaration	Expression	Value
int num	sizeof(num)	2
long num	sizeof(num)	4
float num	sizeof(num)	4
char ch	sizeof(ch)	1
double num	sizeof(num)	8
int a, b;	sizeof(a+2*b)	2

 

EXPRESSIONS :

It is a combination of operators and operands that computes to a specific value. There are three types of expressions.

1.         Arithmetic Expression

2.         Relational Expression

3.         Logical Expression

 

1] ARITHMETIC EXPRESSIONS

An expression involving arithmetic operators is called an arithmetic expression. It takes one or more operands and connects them by an arithmetic operator. These operands are either integers or floating point numbers.

 

EVALUATION OF ARITHMETIC EXPRESSION

Arithmetic expressions are evaluated from left to right. Expressions involving high priority operators are evaluated first.

Rules for evaluation of arithmetic expressions :

1)        If the given expression involves parentheses, then the expressions inside the parenthesis must be evaluated first.

2)        If a unary minus is present in the expressions, then the term associated with unary minus must be evaluated before the other expressions.

 

Precedence and associativity of arithmetic operators

Precedence Level	Operators	Associativity
1	( ) expressions inside the brackets
2	Exponent
3	++, - -, unary minus ( - )	Right to Left
4	*, /, %	Left to Right
5	+, -	Left to Right

Example :

1.  3abc                            =          3 * a * b * c

2.  2(a+bc)                       =          2 * ( a + b * c)

3. s+y z

=           ( x + y ) / z

4.   2p² + 3p + 1                 =          2 * p * p + 3 * p + 1

5.   ( 2x + 1 )( 3y + z )      =          ( 2 * x + 1 ) * ( 3 * y + z )

6.   √a + b                        =          sqrt ( a + b )

7.

(a+b) (a–b)

=          ( a + b ) / ( a – b )

 

Evaluate the following expression :

X	=	9 – 12 / ( 3 + 3 ) * ( 2 – 1 )
X	=	9 – 12 / 6 * 1
X	=	9 – 2 * 1
X	=	9 – 2
X	=	7

 

2] RELATIONAL EXPRESSIONS

A relational expression in a valid combination of variables, constant and relational operators. Generally relational expressions compare the values of two variables or expressions, through relational operators. These operators are used to construct expressions that evaluate to true or false.

Relational operators, their precedence and associativity for evaluation of an expression.

Operator	Meaning	Precedence	Associativity
<	Lesser than	1	Left to Right
< =	Lesser than or Equal to	1	Left to Right
>	Greater than	1	Left to Right
> =	Greater than or Equal to	1	Left to Right
= =	Equal to	2	Left to Right
! =	Not equal to	2	Left to Right

 

Syntax :           Expression1 Relational operator Expression2

Where, Expression1 and Expression2 are arithmetic expressions, which may be simple constants, variable or combination of them.

 

Example :

4.5       < =       10        -           TRUE

4.5       >          10        -           FALSE

A+B = = C + D           -           TRUE if the sum of (A+B) is equal to (C+D)

 

3] LOGICAL EXPRESSIONS

Expressions involving the logical operators are called Logical Expressions. The result of a logical expression is either TRUE (Non-Zero) or FALSE (Zero). The logical expression involves AND ( && ), OR ( | | ) and NOT ( ! ) operators.

 

Operator	Meaning	Precedence	Associativity
&& (double ampersand)	Logical AND	2	L to R
|| (double pipeline)	Logical OR	3	L to R
! (exclamation)	Logical NOT	1	L to R

Example :       ( marks > = 35 ) && ( marks < = 100) ( ch > = ‘A’) & & ( ch < = ‘Z’)

TYPE CONVERSION

In some applications, we may often want to change the data type of the variable. When we declare some variable as int, the desired output may be float or vice versa. In such situations, we  may change the nature of data stored in a variable. This process is known as data type conversion. It is also called type casting.

The process of converting one predefined type into another is called type conversion. There are two types.

1.         Implicit type conversion

2.         Explicit type conversion

 

IMPLICIT TYPE CONVERSION :

This conversion performed by compiler without programmers intervention. This conversion is applied generally whenever different data types are intermixed in an expression.

 

Assignment	Conversion	Result
int = float	Converts float into int by truncating the fraction part	int x; foat y=25.5543; x=y; value of x is 25.
float = int	Converts int to float by adding zeros to the fractional part	float y; y = 10; value of y is 10.000000
double = float	Converts float to double by addition fractional part with across.	float x = 5.123456; double y; y = x; The value of y ix 5.1234560000
float = double	Double value is rounded to the precision of float before truncating	float x; double y = 2.5678987650; x=y; The value x is 2.567899
int = char char = int	Assign the ASCII code of char to int. Assign the ASCII code of int to char	int x; x = ‘A’ value of x is 65 char a; a = 65; value of a is ‘A’

 

EXPLICIT TYPE CONVERSION :

The implicit type conversions are automatic. However, a user can convert data explicitly by type casting.

 

The general form of type casting is as follows :

(data type) expression; Where,

data type – any basic data type and must be written within the parentheses.

Example :

n1 = ( int ) 25.5;

n2 = ( int ) 20.5 / ( int ) 5.5; n3 = ( int ) ( p+q )

n4 = ( int ) p + q

MATHEMATICAL FUNCTIONS

There are certain functions which are readily available in the language. C itself are called library functions.

C provides a large number of library functions which perform specific operations. In C all mathematical functions are enclosed in the header file math.h. Mathematical functions are also included among these library functions.

Function	Purpose	Usage
sin(x)	Sin of x, x is radians	If d=60, x=d*3.142/180, y=sin(x)
cos(x)	Cosine of x, x in radians	If d=60, x=d*3.142/180, y=cos(x)
tan(x)	Tangent of x, x in radians	If d=60, x=d*3.142/180, y=tan(x)
exp(x)	E raised to the power of x (e = 2.718282)	If x = 2.5, y=exp(x)
log(x)	Natural logarithm of x (base e)	y=log(3.0)
log10(x)	Base 10 logarithm of x	y=log10(3.0)
pow(x, y)	X raised to the power y, i.e., XY	y=pow(3,4)
sqrt(x)	Square root of x	y=sqrt(25)
fabs(x)	Absolute value of x	y=fabs(-3.14)
ciel(x)	Rounds x up to the nearest integer	y=ciel(2.339)
floor(x)	Rounds x down to the nearest integer	y=floor(3.339)

 

Transfer the following mathematical expressions in to C expressions :

 

1. √a + b + c	=	sqrt ( a + b + c )
2. ( a + b ) 4	=	pow ( a+b, 4 )
3. Log10 (x/y + c)	=	log ( x/y + c )