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) 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

## 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:

bitwise complement of N = ~N (represented in 2's complement form) 2'complement of ~N= -(~(~N)+1) = -(N+1)

### Example #4: Bitwise complement

```
#include <stdio.h>
int main()
{
printf("Output = %d\n",~35);
printf("Output = %d\n",~-12);
return 0;
}
```

**Output**

Output = -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 specified 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 a certain number of specified bits. The bit positions that have been vacated by the left shift operator are filled with 0. The symbol of the left shift operator is <<.

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

```
#include <stdio.h>
int main()
{
int num=212, i;
for (i=0; i<=2; ++i)
printf("Right shift by %d: %d\n", i, num>>i);
printf("\n");
for (i=0; i<=2; ++i)
printf("Left shift by %d: %d\n", i, num<<i);
return 0;
}
```

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