# Calculate the Hamming Distance between two Integers

##### Problem Statement

Given two integers, calculate the hamming distance between them.

###### Solution Explanation

Hamming Distance between integers is defined as the number of indexes where the two bits differ.

For example, given integers x = 2 and y=5, the hamming distance between them is,

```
X 0 0 1 0
Y 0 1 1 0
HD 0 1 0 1 Total - 1
```

As you see the integers 2 and 5 differ in only 1 bit position, so the hamming distance between them is 1. If you look at this, basically we are doing a XOR operation on each bit and returing the total value as hamming distance.

So, we can just do an XOR between the two given integers and do a bit count and return the value.

Below is the java implementation for hamming distance cacluclation between two integers,

```
public class HammingDistance {
public static void main(String[] args){
HammingDistance hd = new HammingDistance();
System.out.println("Hamming distance between 2 and 5 is "+hd.hammingDistance(2,5));
}
public int hammingDistance(int x, int y) {
int xor = x ^ y;
return Integer.bitCount(xor);
}
}
```

Once we have the xor of the 2 integers, we need the number of 1's in the resultant binary version. To calculate that we use a inbuilt java method Integer.bitCount.

Alternatively, you can also manually calculate the bit count by continously right shifting the resultant xor value and doing an '&' with 1.

Below is the code to avoid using the inbuilt java method and find out the number of 1's,

```
public class HammingDistance {
public static void main(String[] args){
HammingDistance hd = new HammingDistance();
System.out.println("Hamming distance between 2 and 5 is "+hd.hammingDistance(2,5));
}
public int hammingDistance(int x, int y) {
int xor = x ^ y;
int bitCount = 0;
for(int i=0;i<32;i++){
bitCount += (xor >> i) & 1;
}
return bitCount;
}
}
```

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