## Quick links

We use Bitwise operators to manipulate data at its lowest level (bit level). Bitwise operators works on each bit of the data.

Data in the memory (RAM) is organized as a sequence of bytes. Each byte is a group of eight consecutive bits. Bitwise operators are useful when we need to perform actions on bits of the data.

Bitwise operators work with integer type. **They do not support float or real types.**

C has six Bitwise operators.

Operator | Description |
---|---|

`&` | Bitwise AND |

`|` | Bitwise OR |

`^` | Bitwise XOR |

`~` | Bitwise complement |

`<<` | Bitwise left shift |

`>>` | Bitwise right shift |

## Bitwise AND `&`

operator

Bitwise AND is a binary operator. It sets each bit of the resultant value as 1 if corresponding bit in both operands is 1.

Suppose `a` and `b` are two integer variables with initial value

`int a=10, b=11;`

Let us re-write integers in 8-bit binary representation

```
a = 0000 1010
b = 0000 1011
```

`c = a & b`

The above expression `a & b`

will evaluate to `0000 1010` which is 10 in decimal.

```
a 0000 1010
b 0000 1011
-----------------
a & b 0000 1010
```

Bitwise AND operator is used extensively to check whether a particular bit of data is on (1) or off (0).

**Important Note:** As a beginner do not get confused with bitwise AND `&`

with logical AND `&&`

.

## Bitwise OR `|`

operator

Bitwise OR is a binary operator. It sets each bit of the resultant value as 1 if corresponding bit of any of its two operand is 1.

Bitwise OR operator is commonly used to set flag bit values.

Suppose `a` and `b` are two integer variables with initial value as.

`int a=2, b=13;`

Let us re-write the integer in 8-bit binary representation.

```
a = 0000 0010
b = 0000 1101
```

`c = a | b`

The above expression `a|b`

will evaluate to `0000 1111` which is 15 in decimal.

```
a 0000 0010
b 0000 1101
-----------------
a | b 0000 1111
```

**Important note:** Do not confuse between bitwise OR `|`

and logical OR `||`

operator.

## Bitwise XOR `^`

operator

Bitwise XOR operator is also binary operator. It sets each bit of the resultant value to 1 whenever the corresponding bits of the two operands differ.

Suppose `a` and `b` are two integer variables with initial value as.

`int a=6, b=13;`

Let us re-write the integers in 8-bit binary representation:

```
a = 0000 0110
b = 0000 1101
```

`c = a ^ b`

The above expression `a^b`

will evaluate to `0000 1011` which is 11 in decimal.

```
a 0000 0110
b 0000 1101
-----------------
a ^ b 0000 1011
```

**Important note:** Do not confuse bitwise XOR `^`

operator as exponential operator. There is no exponential operator supported by C.

## Bitwise complement `~`

operator

Suppose `a` is an integer variable with initial value as.

`int a=2;`

In 8-bit binary representation:

`a = 0000 0010`

`c = ~a`

The above expression `~a`

will evaluate to `1111 1101` which is -3 (Twos complement) in decimal.

```
a 0000 0010
-----------------
~a 1111 1101
```

## Bitwise left shift `<<`

operator

Bitwise left shift is a binary operator. It is used to shift bits to left `n` times. Consider the below example:

`int a=15;`

Which in 8-bit binary will be represented as:

`a = 0000 1111`

`c = a << 3;`

The above expression `a << 3;`

shifts bits of `a` three times to left and evaluates to `0111 1000`

which is 120 in decimal.

```
a 0000 1111
a << 1 0001 1110
a << 2 0011 1100
a << 3 0111 1000
```

Shifting bits to left causes insertion of zero from right and shifting each bit to one position left from its current position. The most significant bit (the left most bit) is dropped off on every left shift.

**Important note: ** Shifting bits to left is also equivalent to multiplying value by 2. You can use bitwise left shift operator if you need to multiply a variable by a power of two.

## Bitwise right shift `>>`

operator

Bitwise right shift is binary operator used to shift bits to right. Consider the below example:

`int a=15;`

Which in 8-bit binary will be represented as:

`a = 0000 1111`

`c = a >> 3`

The above expression `a >> 3`

shifts bits of variable `a`

three times right and will evaluate to `0000 0001`

which is 1 in decimal

```
a 0000 1111
a >> 1 0000 0111
a >> 2 0000 0011
a >> 3 0000 0001
```

C only supports **Arithmetic Right Shift** means instead of pushing 0 at MSB it pushes sign bit. Which means shifting bits to right causes insertion of 0 or 1 depending on the value of Most Significant Bit (sign bit).

After each right shift, the least significant bit (left most bit) is dropped off.

Important note:Shifting bits to right is equivalent to dividing by 2. You can use bitwise right shift operator if you need to divide a number (unsigned number) by power of 2.

In bitwise right shift 1 is inserted from right if the MSB is 1; otherwise 0 is inserted from right. However, in case of bitwise left shift always 0 is inserted from left.

## Recommended Bitwise operator exercises

- Program to find LSB of a number.
- Program to toggle nth bit of a number.
- Program to count trailing zeros in a binary number.
- Program to flip bits of a number.
- Program to swap two numbers using bitwise operators.

Practice more bitwise operator programming problems.

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