Arithmetic Expressions and Precedence

An arithmetic expression is an expression using additions +, subtractions -, multiplications *, divisions / and modulus %.

An expression is a combination of one or more operands, zero or more operators, and zero or more pairs of parentheses.

For example, in the expression:

                           (5 + x)

x and 5 are operands

+ is an operator

( The open parenthesis, which is used to begin parenthetical text

) The close parenthesis

The operators indicate what action or operation to perform. The operands indicate what items to apply the action to.

An operator is a symbol that tells the compiler to perform specific mathematical or logical functions. C language is rich in built-in operators and provides the following types of operators −

Arithmetic Operators
Assignment Operators
Relational Operators
Logical Operators
Bit-wise Operators

Arithmetic Operators

An arithmetic operator performs mathematical operations such as addition, subtraction, multiplication, division etc on numerical values (constants and variables).

The following table shows all the arithmetic operators supported by the C language. Assume variable A holds 10 and variable B holds 20 then:

Example:

Operator	Description	Example
+	Adds two operands.	A + B = 30
−	Subtracts second operand from the first.	A − B = -10
*	Multiplies both operands.	A * B = 200
/	Divides numerator by de-numerator.	B / A = 2
%	Modulus Operator and remainder of after an integer division.	B % A = 0

Example:

// Working of arithmetic operators
#include <stdio.h>
int main()
{
   int a = 9,b = 4, c;
  
   c = a+b;
   printf("a+b = %d \n",c);
   c = a-b;
   printf("a-b = %d \n",c);
   c = a*b;
   printf("a*b = %d \n",c);
   c = a/b;
   printf("a/b = %d \n",c);
   c = a%b;
   printf("Remainder when a divided by b = %d \n",c);

   return 0;
}

Output

a+b = 13
a-b = 5
a*b = 36
a/b = 2
Remainder when a divided by b=1

Assignment Operators

An assignment operator is used for assigning a value to a variable. The most common assignment operator is =

The following table lists the assignment operators supported by the C language:

Examples:

Operator	Description	Example
=	Simple assignment operator. Assigns values from right side operands to left side operand	C = A + B will assign the value of A + B to C
+=	Add AND assignment operator. It adds the right operand to the left operand and assign the result to the left operand.	C += A is equivalent to C = C + A
-=	Subtract AND assignment operator. It subtracts the right operand from the left operand and assigns the result to the left operand.	C -= A is equivalent to C = C - A
*=	Multiply AND assignment operator. It multiplies the right operand with the left operand and assigns the result to the left operand.	C = A is equivalent to C = C A
/=	Divide AND assignment operator. It divides the left operand with the right operand and assigns the result to the left operand.	C /= A is equivalent to C = C / A
%=	Modulus AND assignment operator. It takes modulus using two operands and assigns the result to the left operand.	C %= A is equivalent to C = C % A

Example:

 // Working of assignment operators
 #include <stdio.h>
 int main()
 {
   int a = 5, c;
   c = a;      // c is 5
   printf("c = %d\n", c);
   c += a;     // c is 10 
   printf("c = %d\n", c);
   c -= a;     // c is 5
   printf("c = %d\n", c);
   c *= a;     // c is 25
   printf("c = %d\n", c);
   c /= a;     // c is 5
   printf("c = %d\n", c);
   c %= a;     // c = 0
   printf("c = %d\n", c);
   return 0;
  }

Relational Operators

A relational operator checks the relationship between two operands. If the relation is true, it returns 1; if the relation is false, it returns value 0.

Relational operators are used in decision making and loops.

The following table shows all the relational operators supported by C. Assume variable A holds 10 and variable B holds 20 then −

Example:

Operator	Description	Example
==	Checks if the values of two operands are equal or not. If yes, then the condition becomes true.	(A == B) is not true.
!=	Checks if the values of two operands are equal or not. If the values are not equal, then the condition becomes true.	(A != B) is true.
>	Checks if the value of left operand is greater than the value of right operand. If yes, then the condition becomes true.	(A > B) is not true.
<	Checks if the value of left operand is less than the value of right operand. If yes, then the condition becomes true.	(A < B) is true.
>=	Checks if the value of left operand is greater than or equal to the value of right operand. If yes, then the condition becomes true.	(A >= B) is not true.
<=	Checks if the value of left operand is less than or equal to the value of right operand. If yes, then the condition becomes true.	(A <= B) is true.

Example:

// Working of relational operators
#include <stdio.h>
int main()
{
   int a = 5, b = 5, c = 10;
   printf("%d == %d is %d \n", a, b, a == b);
   printf("%d == %d is %d \n", a, c, a == c);
   printf("%d > %d is %d \n", a, b, a > b);
   printf("%d > %d is %d \n", a, c, a > c);
   printf("%d < %d is %d \n", a, b, a < b);
   printf("%d < %d is %d \n", a, c, a < c);
   printf("%d != %d is %d \n", a, b, a != b);
   printf("%d != %d is %d \n", a, c, a != c);
   printf("%d >= %d is %d \n", a, b, a >= b);
   printf("%d >= %d is %d \n", a, c, a >= c);
   printf("%d <= %d is %d \n", a, b, a <= b);
   printf("%d <= %d is %d \n", a, c, a <= c);
   return 0;
}

Output

== 5 is 1
== 10 is 0
    5> 5 is 0
> 10 is 0
< 5 is 0
< 10 is 1
!= 5 is 0
!= 10 is 1
>= 5 is 1
>= 10 is 0
<= 5 is 1
<= 10 is 1

Logical Operators

An expression containing logical operator returns either 0 or 1 depending upon whether expression results true or false. Logical operators are commonly used in decision making in C programming.

Following table shows all the logical operators supported by C language. Assume variable A holds 1 and variable B holds 0, then −

Example:

Operator	Description	Example
&&	Called Logical AND operator.	If both the operands are non-zero, then the condition becomes true. (A && B) is false.
\|\|	Called Logical OR Operator.	If any of the two operands is non-zero, then the condition becomes true. (A
!	Called Logical NOT Operator.	It is used to reverse the logical state of its operand. If a condition is true, then Logical NOT operator will make it false. !(A && B) is true.

Example:

// Working of logical operators
#include <stdio.h>
int main()
{
  int a = 5, b = 5, c = 10, result;
  result = (a == b) && (c > b);
  printf("(a == b) && (c > b) is %d \n", result);
  result = (a == b) && (c < b);
  printf("(a == b) && (c < b) is %d \n", result);
  result = (a == b) || (c < b);
  printf("(a == b) || (c < b) is %d \n", result);
  result = (a != b) || (c < b);
  printf("(a != b) || (c < b) is %d \n", result);
  result = !(a != b);
  printf("!(a == b) is %d \n", result);
  result = !(a == b);
  printf("!(a == b) is %d \n", result);
  return 0;
}

Output

    (a == b) && (c > b) is 1 
    (a == b) && (c < b) is 0 
    (a == b) || (c < b) is 1 
    (a != b) || (c < b) is 0 
    !(a != b) is 1 
    !(a == b) is 0 

Explanation of logical operator program

    (a == b) && (c > 5) evaluates to 1 because both operands (a == b) and (c > b) is 1 (true).
    (a == b) && (c < b) evaluates to 0 because operand (c < b) is 0 (false).
    (a == b) || (c < b) evaluates to 1 because (a = b) is 1 (true).
    (a != b) || (c < b) evaluates to 0 because both operand (a != b) and (c < b) are 0 (false).
    !(a != b) evaluates to 1 because operand (a != b) is 0 (false). Hence, !(a != b) is 1 (true).
    !(a == b) evaluates to 0 because (a == b) is 1 (true). Hence, !(a == b) is 0 (false).

Bitwise Operators

During computation, mathematical operations like: addition, subtraction, multiplication, division, etc are converted to bit-level which makes processing faster and saves power.

Bitwise operators are used in C programming to perform bit-level operations.

Bitwise operator works on bits and perform bit-by-bit operation. The truth tables for &, |, and ^ is as follows − & Bitwise AND | Bitwise OR ^ Bitwise exclusive OR ~ Bitwise complement « Shift left >>Shift right

p	q	p & q	p \| q	p^q
0	0	0	0	0
0	1	0	1	1
1	1	1	1	0
1	0	0	1	1

Assume A = 60 and B = 13 in binary format, they will be as follows −

A = 0011 1100

B = 0000 1101

A&B = 0000 1100

A	B = 0011 1101

A^B = 0011 0001

~A = 1100 0011

The following table lists the bitwise operators supported by C. Assume variable ‘A’ holds 60 and variable ‘B’ holds 13, then −

Example:

Operator	Description	Example
&	Binary AND Operator copies a bit to the result if it exists in both operands.	(A & B) = 12, i.e., 0000 1100
\|	Binary OR Operator copies a bit if it exists in either operand.	(A \| B) = 61, i.e., 0011 1101
^	Binary XOR Operator copies the bit if it is set in one operand but not both.	(A ^ B) = 49, i.e., 0011 0001
~	Binary One’s Complement Operator is unary and has the effect of ‘flipping’ bits.	(~A ) = ~(60), i.e,. -0111101
«	Binary Left Shift Operator. The left operands value is moved left by the number of bits specified by the right operand.	A « 2 = 240 i.e., 1111 0000
»	Binary Right Shift Operator. The left operands value is moved right by the number of bits specified by the right operand.	A » 2 = 15 i.e., 0000 1111

Let us suppose the bitwise AND operation of two integers 12 and 25.

    12 = 00001100 (In Binary)
    25 = 00011001 (In Binary)

    Bit Operation of 12 and 25
      00001100
    & 00011001
      ________
      00001000  = 8 (In decimal)

Example #1: Bitwise AND

    #include <stdio.h>
    int main()
    {
        int a = 12, b = 25;
        printf("Output = %d", a&b);
        return 0;
    } Output

    Output = 8

Bitwise OR operator |

The output of bitwise OR is 1 if at least one corresponding bit of two operands is 1. In C Programming, bitwise OR operator is denoted by |.

    12 = 00001100 (In Binary)
    25 = 00011001 (In Binary)

Bitwise OR Operation of 12 and 25

      00001100
    | 00011001
      ________
      00011101  = 29 (In decimal)

Example #2: Bitwise OR

    #include <stdio.h>
    int main()
    {
        int a = 12, b = 25;
        printf("Output = %d", a|b);
        return 0;
    } Output

    Output = 29

Bitwise XOR (exclusive OR) operator ^

The result of bitwise XOR operator is 1 if the corresponding bits of two operands are opposite. It is denoted by ^.

    12 = 00001100 (In Binary)
    25 = 00011001 (In Binary)

Bitwise XOR Operation of 12 and 25

      00001100
    ^ 00011001
      ________
      00010101  = 21 (In decimal)

Example #3: Bitwise XOR

    #include <stdio.h>
    int main()
    {
        int a = 12, b = 25;
        printf("Output = %d", a^b);
        return 0;
    } Output

    Output = 21

Misc Operators

The sizeof operator

The sizeof is a unary operator that returns the size of data (constants, variables, array, structure, etc).

Example : sizeof Operator

    #include <stdio.h>
    int main()
    {
        int a;
        float b;
        double c;
        char d;
        printf("Size of int=%lu bytes\n",sizeof(a));
        printf("Size of float=%lu bytes\n",sizeof(b));
        printf("Size of double=%lu bytes\n",sizeof(c));
        printf("Size of char=%lu byte\n",sizeof(d));
        return 0;
    } Output

    Size of int = 4 bytes
    Size of float = 4 bytes
    Size of double = 8 bytes
    Size of char = 1 byte

Operator Precedence and Associativity

Operator precedence determines the grouping of terms in an expression and decides how an expression is evaluated. Certain operators have higher precedence than others; for example, the multiplication operator has a higher precedence than the addition operator.

    For example, 
       x = 7 + 3 * 2; here, x is assigned 13, not 20 because operator * has
       a higher precedence than +, so it first gets multiplied with 3*2 and 
       then adds into 7.

Here, operators with the highest precedence appear at the top of the table, those with the lowest appear at the bottom. Within an expression, higher precedence operators will be evaluated first.

Category	Operator	Associativity
Postfix	( ) [ ] . ++ - -	Left to right
Unary	+ - ! ~ ++ - - (type) * & sizeof	Right to left
Multiplicative	* / %	Left to right
Additive	+ -	Left to right
Relational	< <= > >=	Left to right
Equality	== !=	Left to right
Bitwise AND	&	Left to right
Bitwise XOR	^	Left to right
Bitwise OR	\|	Left to right
Logical AND	&&	Left to right
Logical OR	\|\|	Left to right
Conditional	? :	Right to left
Assignment	= += -= *= /= %= »= «= &= ^= \|=	Right to left
Comma	,	Left to right

Example

Try the following example to understand operator precedence in C −

     #include <stdio.h>

      int main() 
      {

       int a = 20;
       int b = 10;
       int c = 15;
       int d = 5;
       int e;
 
       e = (a + b) * c / d;                                  // ( 30 * 15 ) / 5
       printf("Value of (a + b) * c / d is : %d\n",  e );

       e = ((a + b) * c) / d;                                // (30 * 15 ) / 5
       printf("Value of ((a + b) * c) / d is  : %d\n" ,  e );

       e = (a + b) * (c / d);                                 // (30) * (15/5)
       printf("Value of (a + b) * (c / d) is  : %d\n",  e );

       e = a + (b * c) / d;                                  //  20 + (150/5)
       printf("Value of a + (b * c) / d is  : %d\n" ,  e );
  
       return 0;
      }

When you compile and execute the above program, it produces the following result −

    Value of (a + b) * c / d is : 90
    Value of ((a + b) * c) / d is  : 90
    Value of (a + b) * (c / d) is  : 90
    Value of a + (b * c) / d is  : 50

Operators Associativity is used when two operators of same precedence appear in an expression. Associativity can be either Left to Right or Right to Left.

For example: ‘*’ and ‘/’ have same precedence and their associativity is Left to Right, so the expression “100 / 10 * 10” is treated as “(100 / 10) * 10”.

Operators Precedence and Associativity are two characteristics of operators that determine the evaluation order of sub-expressions in absence of brackets.

PPS

Programming for Problem Solving