7/15/2017 C Bitwise Operators: AND, OR, XOR, Complement and Shift Operations

Bitwise Operators in C Programming

In this tutorial you will learn about all 6 bitwise operators in C programming with examples.

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In arithmetic-logic unit  (which is within the CPU), mathematical operations like: addition, subtraction, multiplication and division are done
in bit-level. To perform bit-level operations in C programming, bitwise operators are used. 

Operators Meaning of operators

& Bitwise AND

| Bitwise OR

^ Bitwise XOR

~ Bitwise complement

<< Shift left

>> Shift right

Bitwise AND operator &

The output of bitwise AND is 1 if the corresponding bits of two operands is 1. If either bit of an operand is 0, the result of
corresponding bit is evaluated to 0.

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

12 = 00001100 (In Binary)

25 = 00011001 (In Binary)

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Bit Operation of 12 and 25 

00001100
& 00011001
________
00001000 = 8 (In decimal)

Example #1: Bitwise AND

run

input output

1 #include <stdio.h>
2 int main()
3 {
4 int a = 12, b = 25;
5 printf("Output = %d", a&b);
6 return 0;
7 }

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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

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7/15/2017 C Bitwise Operators: AND, OR, XOR, Complement and Shift Operations

run 
input output

1 #include <stdio.h>
2 int main()
3 {
4 int a = 12, b = 25;
5 printf("Output = %d", a|b);
6 return 0;
7 }

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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

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run 
input output

1 #include <stdio.h>
2 int main()
3 {
4 int a = 12, b = 25;
5 printf("Output = %d", a^b);
6 return 0;
7 }

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Output

Output = 21

Bitwise complement operator ~

Bitwise compliment operator is an unary operator (works on only one operand). It changes 1 to 0 and 0 to 1. It is denoted by ~.

35 = 00100011 (In Binary)

Bitwise complement Operation of 35

~ 00100011
________
11011100 = 220 (In decimal)

Twist in bitwise complement operator in C Programming

The bitwise complement of 35 (~35) is -36 instead of 220, but why?

For any integer n , bitwise complement of n will be -(n+1) . To understand this, you should have the knowledge of 2's complement.

2's Complement
Two's complement is an operation on binary numbers. The 2's complement of a number is equal to the complement of that number plus
1. For example:

Decimal Binary 2's complement

0 00000000 -(11111111+1) = -00000000 = -0(decimal)
1 00000001 -(11111110+1) = -11111111 = -256(decimal)
12 00001100 -(11110011+1) = -11110100 = -244(decimal)
220 11011100 -(00100011+1) = -00100100 = -36(decimal)

Note: Overflow is ignored while computing 2's complement.

The bitwise complement of 35 is 220 (in decimal). The 2's complement of 220 is -36. Hence, the output is -36 instead of 220.

Bitwise complement of any number N is -(N+1). Here's how:

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bitwise complement of N = ~N (represented in 2's complement form) 

2'complement of ~N= -(~(~N)+1) = -(N+1)

Example #4: Bitwise complement

run

input output

1 #include <stdio.h>
2 int main()
3 {
4 printf("complement = %d\n",~35);
5 printf("complement = %d\n",~-12);
6 return 0;
7 }

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Output

complement = -36
Output = 11

Shift Operators in C programming

There are two shift operators in C programming:

Right shift operator

Left shift operator.

Right Shift Operator

Right shift operator shifts all bits towards right by certain number of speci ed bits. It is denoted by >>.

212 = 11010100 (In binary)

212>>2 = 00110101 (In binary) [Right shift by two bits]
212>>7 = 00000001 (In binary)
212>>8 = 00000000
212>>0 = 11010100 (No Shift)

Left Shift Operator

Left shift operator shifts all bits towards left by certain number of speci ed bits. It is denoted by <<.

212 = 11010100 (In binary)

212<<1 = 110101000 (In binary) [Left shift by one bit]
212<<0 =11010100 (Shift by 0)
212<<4 = 110101000000 (In binary) =3392(In decimal)

Example #5: Shift Operators

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Example #5: Shift Operators


run

input output

1 #include <stdio.h>
2 int main()
3 {
4 int num=212, i;
5 for (i=0; i<=2; ++i)
6 printf("Right shift by %d: %d\n", i, num>>i);
7
8 printf("\n");
9
10 for (i=0; i<=2; ++i)
11 printf("Left shift by %d: %d\n", i, num<<i);
12
13 return 0;
14 }

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Right Shift by 0: 212

Right Shift by 1: 106
Right Shift by 2: 53

Left Shift by 0: 212

Left Shift by 1: 424
Left Shift by 2: 848

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