Position of rightmost different bit

Difficulty Level : Easy
Last Updated : 01 Jul, 2021

Given two numbers m and n. Find the position of the rightmost different bit in the binary representation of numbers. It is guaranteed that such a bit exists.

Examples:

Input: m = 11, n = 9
Output: 2
(11)₁₀ = (1011)₂
(9)₁₀ = (1001)₂
It can be seen that 2nd bit from
the right is different 

Input: m = 52, n = 4
Output: 5
(52)₁₀ = (110100)₂
(4)₁₀ = (100)₂, can also be written as
     = (000100)₂
It can be seen that 5th bit from
the right is different

Recommended Practice

Rightmost different bit

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Approach: Get the bitwise xor of m and n. Let it be xor_value = m ^ n. Now, find the position of rightmost set bit in xor_value.

Explanation: The bitwise xor operation produces a number that has set bits only at the positions where the bits of m and n differ. Thus, the position of the rightmost set bit in xor_value gives the position of the rightmost different bit.

Efficient way to find the rightmost set bit: 
log_{2(n & -n) + 1}gives us the position of the rightmost set bit.
(-n) reverses all the bits from left to right till the last set bit
for example:
n = 168₁₀
binary signed 2's complement of n  = 0000000010101000₂
binary signed 2's complement of -n = 1111111101011000₂
∴ (n & -n) = 0000000000001000₂ = 8
now, log₂(n & -n) = log₂(8) = 3
log2(n & -n) + 1 = 4 (position of rightmost set bit)

Below is the implementation of the above approach:

C++

// C++ implementation to find the position
// of rightmost different bit
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the position of
// rightmost set bit in 'n'
// returns 0 if there is no set bit.
int getRightMostSetBit(int n)
{
    // to handle edge case when n = 0.  
    if (n == 0)  
        return 0;
     
    return log2(n & -n) + 1;
}
 
// Function to find the position of
// rightmost different bit in the
// binary representations of 'm' and 'n'
// returns 0 if there is no 
// rightmost different bit.
int posOfRightMostDiffBit(int m, int n)
{
    // position of rightmost different
    //  bit
     
    return getRightMostSetBit(m ^ n);
}
 
// Driver program
int main()
{
    int m = 52, n = 24;
   
    cout << "Position of rightmost different bit:"
         << posOfRightMostDiffBit(m, n)<<endl;
    return 0;
}

Java

// Java implementation to find the position
// of rightmost different bit
 
class GFG {
     
    // Function to find the position of
    // rightmost set bit in 'n'
    // return 0 if there is no set bit.
    static int getRightMostSetBit(int n) 
    {
        if(n == 0)
          return 0;
       
        return (int)((Math.log10(n & -n)) / 
                     Math.log10(2)) + 1;
    }
     
    // Function to find the position of
    // rightmost different bit in the
    // binary representations of 'm' and 'n'
    static int posOfRightMostDiffBit(int m, int n) 
    {
        // position of rightmost different bit
        return getRightMostSetBit(m ^ n);
    }
     
    // Driver code
    public static void main(String arg[])
    {
        int m = 52, n = 4;
        System.out.print("Position = " + 
            posOfRightMostDiffBit(m, n));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3

# Python implementation
# to find the position
# of rightmost different bit
 
import math
 
# Function to find the position of 
# rightmost set bit in 'n'
def getRightMostSetBit(n):
    if (n == 0):
        return 0
 
    return math.log2(n & -n) + 1
 
 
# Function to find the position of 
# rightmost different bit in the 
# binary representations of 'm' and 'n'
def posOfRightMostDiffBit(m, n):
 
    # position of rightmost different
    # bit
    return getRightMostSetBit(m ^ n)
 
# Driver code
 
m = 52
n = 4
print("position = ", int(posOfRightMostDiffBit(m, n)))
 
# This code is contributed
# by Anant Agarwal.

C#

// C# implementation to find the position
// of rightmost different bit
using System;
 
class GFG {
     
    // Function to find the position of
    // rightmost set bit in 'n'
    static int getRightMostSetBit(int n) 
    {
        if (n == 0)
            return 0;
        return (int)((Math.Log10(n & -n))
                       / Math.Log10(2)) + 1;
    }
     
    // Function to find the position of
    // rightmost different bit in the
    // binary representations of 'm' and 'n'
    static int posOfRightMostDiffBit(int m, int n) 
    {
        // position of rightmost different bit
        return getRightMostSetBit(m ^ n);
    }
     
    // Driver code
    public static void Main()
    {
        int m = 52, n = 4;
        Console.Write("Position = " + 
            posOfRightMostDiffBit(m, n));
    }
}
 
// This code is contributed by Smitha.

PHP

<?php
// PHP implementation to 
// find the position of
// rightmost different bit
 
// Function to find the position 
// of rightmost set bit in 'n'
function getRightMostSetBit($n)
{
    if ($n == 0)
      return 0;
    return log($n & -$n, (2)) + 1;
}
 
// Function to find the position of 
// rightmost different bit in the 
// binary representations of 'm' 
// and 'n'
function posOfRightMostDiffBit($m, $n)
{
     
    // position of rightmost
    // different bit
    return getRightMostSetBit($m ^ $n);
}
 
    // Driver Code
    $m = 52;
    $n = 4;
    echo posOfRightMostDiffBit($m, $n);
         
// This code is contributed by Ajit
?>

Javascript

<script>
// JavaScript implementation to find the position
// of rightmost different bit
 
// Function to find the position of
// rightmost set bit in 'n'
// returns 0 if there is no set bit.
function getRightMostSetBit(n)
{
 
    // to handle edge case when n = 0.
    if (n == 0)
        return 0;
     
    return Math.log2(n & -n) + 1;
}
 
// Function to find the position of
// rightmost different bit in the
// binary representations of 'm' and 'n'
// returns 0 if there is no
// rightmost different bit.
function posOfRightMostDiffBit(m, n)
{
    // position of rightmost different
    // bit
     
    return getRightMostSetBit(m ^ n);
}
 
// Driver program
 
    let m = 52, n = 24;
 
    document.write("Position of rightmost different bit:"
        + posOfRightMostDiffBit(m, n) + "<br>");
 
 
 
// This code is contributed by Surbhi Tyagi.
</script>

Output

Position of rightmost different bit:3

Using ffs() function

C++

// C++ implementation to find the
// position of rightmost different
// bit in two number.
#include <bits/stdc++.h>
using namespace std;
  
// function to find rightmost different
//  bit in two numbers.
int posOfRightMostDiffBit(int m, int n)
{
    return ffs(m ^ n);
}
  
// Driver code
int main()
{
    int m = 52, n = 4;
    cout <<"Position = " << 
         posOfRightMostDiffBit(m, n);
    return 0; 
} 

Java

// Java implementation to find the
// position of rightmost different
// bit in two number.
import java.util.*;
class GFG{
  
// function to find rightmost 
// different bit in two numbers.
static int posOfRightMostDiffBit(int m, 
                                 int n)
{
  return (int)Math.floor(
              Math.log10(
              Math.pow(m ^ n, 
                       2)))+2;
}
  
// Driver code
public static void main(String[] args)
{
  int m = 52, n = 4;
  System.out.println("Position = " +  
                     posOfRightMostDiffBit(m, n));
} 
} 
 
// This code is contributed by gauravrajput1

Python3

# Python3 implementation to find the
# position of rightmost different
# bit in two number.
from math import floor, log10
 
# Function to find rightmost different
# bit in two numbers.
def posOfRightMostDiffBit(m, n):
     
    return floor(log10(pow(m ^ n, 2))) + 2
 
# Driver code
if __name__ == '__main__':
     
    m, n = 52, 4
     
    print("Position = ", 
    posOfRightMostDiffBit(m, n))
 
# This code is contributed by mohit kumar 29

C#

// C# implementation to find the
// position of rightmost different
// bit in two number.
using System;
class GFG
{
 
  // function to find rightmost 
  // different bit in two numbers.
  static int posOfRightMostDiffBit(int m,
                                   int n)
  {
    return (int)Math.Floor(Math.Log10(
      Math.Pow(m ^ n, 2))) + 2;
  }
 
  // Driver code
  public static void Main(String[] args)
  {
    int m = 52, n = 4;
    Console.Write("Position = " + 
                  posOfRightMostDiffBit(m, n));
  } 
} 
 
// This code is contributed by shivanisinghss2110

PHP

<?php
// PHP implementation to find the
// position of rightmost different
// bit in two number.
 
// function to find rightmost 
// different bit in two numbers.
function posOfRightMostDiffBit($m, $n)
{
    $t = floor(log($m ^ $n, 2));
    return $t;
}
 
// Driver code
$m = 52;
$n = 4;
echo "Position = " , 
    posOfRightMostDiffBit($m, $n);
 
// This code is contributed by ajit
?>

Javascript

<script>
 
    // Javascript implementation to find the
    // position of rightmost different
    // bit in two number.
     
    // function to find rightmost
    // different bit in two numbers.
    function posOfRightMostDiffBit(m, n)
    {
      return parseInt(Math.floor
      (Math.log10(Math.pow(m ^ n, 2))), 10) + 2;
    }
     
    let m = 52, n = 4;
    document.write(
    "Position = " + posOfRightMostDiffBit(m, n)
    );
     
</script>

Output

Position = 5

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Position of rightmost different bit

C++

Java

Python3

C#

PHP

Javascript

C++

Java

Python3

C#

PHP

Javascript

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