# Left and Right Bit Rotation using Bitwise Operators

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A bitwise operation involves manipulation of one or more bits of a bit pattern. A bitwise operation can simply be done using bitwise operators. In reality, what actually happens is that the decimal number is converted to a binary number internally by the processor and then manipulation takes place on a bit level. In bit rotation, the bits are shifted to the direction specified.

Bit rotation is of two types:

**Left Bitwise Rotation**: In this scenario, the bits are shifted to the left.**Right Bitwise Rotation**:In this scenario, the bits are shifted to the right.

### Left Rotation by 1 bit

Suppose we want to left rotate the number(n) 16 by 1 bit position(d).The number is represented in 8 bit as **00010000** and then shifting takes place as shown below. After shifting the obtained number is **00100000** which on converting to decimal is equivalent to 64.It is therefore observed that on left shifting a number, the result(l) is:

##### l = n * (2^d)

### Right Rotation by 1 bit

Suppose we want to left rotate the number(n) 16 by 1 bit position(d).The number is represented in 8 bit as **00010000** and then shifting takes place as shown below. After shifting the obtained number is **00001000** which on converting to decimal is equivalent to 8.It is therefore observed that on left shifting a number, the result(r) is:

##### r = n / (2^d)

### Pseudocode

```
Procedure rotateLeft(int,int):
1. Start
2. Calculate c=(n << d) | (n >> (tot_bits - d))
3. Return the value of c
4. End
Procedure rotateRight(int,int):
1. Start
2. Calculate c=(n >> d) | (n << (tot_bits - d))
3. Return the value of c
4. End
```

### Implementation

- Java

### Java

```
//Program to rotate bits of a number using bitwise operators
import java.io.*;
class RotateBits
{
BufferedReader xy=new BufferedReader(new InputStreamReader(System.in));
int tot_bits = 32;
//This function is used to rotate the number n by d bits in the left direction
int rotateLeft(int n, int d)
{
int c=(n << d) | (n >> (tot_bits - d));
return c;
}
//This function is used to rotate the number n by d bits in the right direction
int rotateRight(int n, int d)
{
int c=(n >> d) | (n << (tot_bits - d));
return c;
}
public void main(String arg[]) throws IOException
{
System.out.println("Enter the number");
int num = Integer.parseInt(xy.readLine());
System.out.println("Enter the number of bits by which it is to be shifted");
int bits = Integer.parseInt(xy.readLine());
System.out.print("Left Rotation of " + num +
" by " + bits + " is ");
System.out.print(rotateLeft(num, bits));
System.out.print("\nRight Rotation of " + num +
" by " + bits + " is ");
System.out.print(rotateRight(num, bits));
}
}
```

### Applications

- We can perform multiplication by a number raised to the power of 2 by doing left rotation bitwise operation.
- We can perform division by a number raised to the power of 2 by doing rigt rotation bitwise operation.