Swap bits in a given number

Given a number x and two positions (from the right side) in the binary representation of x, write a function that swaps n bits at given two positions and returns the result. It is also given that the two sets of bits do not overlap.

Method 1
Let p1 and p2 be the two given positions.

Example 1

Input:
x = 47 (00101111)
p1 = 1 (Start from the second bit from the right side)
p2 = 5 (Start from the 6th bit from the right side)
n = 3 (No of bits to be swapped)
Output:
227 (11100011)
The 3 bits starting from the second bit (from the right side) are 
swapped with 3 bits starting from 6th position (from the right side) 

Example 2

Input:
x = 28 (11100)
p1 = 0 (Start from first bit from right side)
p2 = 3 (Start from 4th bit from right side)
n = 2 (No of bits to be swapped)
Output:
7 (00111)
The 2 bits starting from 0th position (from right side) are
swapped with 2 bits starting from 4th position (from right side) 

Solution
We need to swap two sets of bits. XOR can be used in a similar way as it is used to swap 2 numbers. Following is the algorithm.



1) Move all bits of the first set to the rightmost side
   set1 =  (x >> p1) & ((1U << n) - 1)
Here the expression (1U << n) - 1 gives a number that 
contains last n bits set and other bits as 0. We do & 
with this expression so that bits other than the last 
n bits become 0.
2) Move all bits of second set to rightmost side
   set2 =  (x >> p2) & ((1U << n) - 1)
3) XOR the two sets of bits
   xor = (set1 ^ set2) 
4) Put the xor bits back to their original positions. 
   xor = (xor << p1) | (xor << p2)
5) Finally, XOR the xor with original number so 
   that the two sets are swapped.
   result = x ^ xor

Implementation:

C++

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// C++ Program to swap bits
// in a given number
#include <bits/stdc++.h>
using namespace std;
  
int swapBits(unsigned int x, unsigned int p1,
             unsigned int p2, unsigned int n)
{
    /* Move all bits of first set to rightmost side */
    unsigned int set1 = (x >> p1) & ((1U << n) - 1);
  
    /* Move all bits of second set to rightmost side */
    unsigned int set2 = (x >> p2) & ((1U << n) - 1);
  
    /* Xor the two sets */
    unsigned int Xor = (set1 ^ set2);
  
    /* Put the Xor bits back to their original positions */
    Xor = (Xor << p1) | (Xor << p2);
  
    /* Xor the 'Xor' with the original number so that the 
    two sets are swapped */
    unsigned int result = x ^ Xor;
  
    return result;
}
  
/* Driver code*/
int main()
{
    int res = swapBits(28, 0, 3, 2);
    cout << "Result = " << res;
    return 0;
}
  
// This code is contributed by rathbhupendra

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C

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// C Program to swap bits
// in a given number
#include <stdio.h>
  
int swapBits(unsigned int x, unsigned int p1, unsigned int p2, unsigned int n)
{
    /* Move all bits of first set to rightmost side */
    unsigned int set1 = (x >> p1) & ((1U << n) - 1);
  
    /* Move all bits of second set to rightmost side */
    unsigned int set2 = (x >> p2) & ((1U << n) - 1);
  
    /* XOR the two sets */
    unsigned int xor = (set1 ^ set2);
  
    /* Put the xor bits back to their original positions */
    xor = (xor << p1) | (xor << p2);
  
    /* XOR the 'xor' with the original number so that the 
       two sets are swapped */
    unsigned int result = x ^ xor;
  
    return result;
}
  
/* Driver program to test above function*/
int main()
{
    int res = swapBits(28, 0, 3, 2);
    printf("\nResult = %d ", res);
    return 0;
}

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Java

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// Java Program to swap bits
// in a given number
  
class GFG {
  
    static int swapBits(int x, int p1, int p2, int n)
    {
        // Move all bits of first set
        // to rightmost side
        int set1 = (x >> p1) & ((1 << n) - 1);
  
        // Move all bits of second set
        // to rightmost side
        int set2 = (x >> p2) & ((1 << n) - 1);
  
        // XOR the two sets
        int xor = (set1 ^ set2);
  
        // Put the xor bits back to
        // their original positions
        xor = (xor << p1) | (xor << p2);
  
        // XOR the 'xor' with the original number
        // so that the  two sets are swapped
        int result = x ^ xor;
  
        return result;
    }
  
    // Driver program
    public static void main(String[] args)
    {
        int res = swapBits(28, 0, 3, 2);
        System.out.println("Result = " + res);
    }
}
  
// This code is contributed by prerna saini.

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Python3

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# Python program to
# swap bits in a given number
  
def swapBits(x, p1, p2, n):
  
    # Move all bits of first
    # set to rightmost side 
    set1 =  (x >> p1) & ((1<< n) - 1)
   
    # Moce all bits of second
    # set to rightmost side 
    set2 =  (x >> p2) & ((1 << n) - 1)
   
    # XOR the two sets 
    xor = (set1 ^ set2)
   
    # Put the xor bits back
    # to their original positions 
    xor = (xor << p1) | (xor << p2)
   
      # XOR the 'xor' with the
      # original number so that the 
      # two sets are swapped
    result = x ^ xor
   
    return result
      
# Driver code
  
res = swapBits(28, 0, 3, 2)
print("Result =", res)
  
# This code is contributed
# by Anant Agarwal.

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C#

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// C# Program to swap bits
// in a given number
using System;
  
class GFG {
  
    static int swapBits(int x, int p1, int p2, int n)
    {
        // Move all bits of first
        // set to rightmost side
        int set1 = (x >> p1) & ((1 << n) - 1);
  
        // Move all bits of second set
        // set to rightmost side
        int set2 = (x >> p2) & ((1 << n) - 1);
  
        // XOR the two sets
        int xor = (set1 ^ set2);
  
        // Put the xor bits back to
        // their original positions
        xor = (xor << p1) | (xor << p2);
  
        // XOR the 'xor' with the original number
        // so that the two sets are swapped
        int result = x ^ xor;
  
        return result;
    }
  
    // Driver program
    public static void Main()
    {
        int res = swapBits(28, 0, 3, 2);
        Console.WriteLine("Result = " + res);
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP Program to swap bits 
// in a given number
  
// function returns
// the swapped bits
function swapBits($x, $p1, $p2, $n)
{
      
    // Move all bits of first 
    // set to rightmost side 
    $set1 = ($x >> $p1) & 
            ((1 << $n) - 1);
  
    // Move all bits of second
    // set to rightmost side 
    $set2 = ($x >> $p2) & 
            ((1 << $n) - 1);
  
    // XOR the two sets 
    $xor = ($set1 ^ $set2);
  
    // Put the xor bits back to 
    // their original positions 
    $xor = ($xor << $p1) | 
           ($xor << $p2);
  
    // XOR the 'xor' with the 
    // original number so that
    // the two sets are swapped 
    $result = $x ^ $xor;
  
    return $result;
}
  
    // Driver Code
    $res = swapBits(28, 0, 3, 2);
    echo "\nResult = ", $res;
      
// This code is contributed by anuj_67.
?>

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Output:

 Result = 7

Following is a shorter implementation of the same logic

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int swapBits(unsigned int x, unsigned int p1, unsigned int p2, unsigned int n)
{
    /* xor contains xor of two sets */
    unsigned int xor = ((x >> p1) ^ (x >> p2)) & ((1U << n) - 1);
  
    /* To swap two sets, we need to again XOR the xor with original sets */
    return x ^ ( (xor << p1) | (xor << p2));
}

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Method 2 –
This solution focuses on calculating the values of bits to be swapped using AND gate. Then we can set/unset those bits based on whether the bits are to be swapped. For the number of bits to be swapped (n) –

  • Calculate shift1 = The value after setting bit at p1 position to 1
  • Calculate shift2 = The value after setting bit at p2 position to 1
  • value1 = Number to check if num at position p1 is set or not.
  • value2 = Number to check if num at position p2 is set or not.
  • If value1 and value2 are different is when we have to swap the bits.

Example:

[28 0 3 2] num=28 (11100) p1=0 p2=3 n=2
   Given = 11100
   Required output = 00111 i.e. (00)1(11) msb 2 bits replaced with lsb 2 bits

n=2
  p1=0,  p2=3
  shift1= 1,  shift2= 1000
  value1= 0,  value2= 1000
 After swap
  num= 10101

n=3
  p1=1,  p2=4
  shift1= 10,  shift2= 10000
  value1= 0,  value2= 10000
 After swap
  num= 00111

Implementation

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#include <iostream>
using namespace std;
  
int swapBits(unsigned int num, unsigned int p1,
             unsigned int p2, unsigned int n)
{
    int shift1, shift2, value1, value2;
    while (n--) {
        // Setting bit at p1 position to 1
        shift1 = 1 << p1;
        // Setting bit at p2 position to 1
        shift2 = 1 << p2;
  
        // value1 and value2 will have 0 if num
        // at the respective positions - p1 and p2 is 0.
        value1 = ((num & shift1));
        value2 = ((num & shift2));
  
        // check if value1 and value2 are different
        // i.e. at one position bit is set and other it is not
        if ((!value1 && value2) || (!value2 && value1)) {
            // if bit at p1 positon is set
            if (value1) {
                // unset bit at p1 position
                num = num & (~shift1);
                // set bit at p2 position
                num = num | shift2;
            }
            // if bit at p2 position is set
            else {
                // set bit at p2 position
                num = num & (~shift2);
                // unset bit at p2 position
                num = num | shift1;
            }
        }
        p1++;
        p2++;
    }
    // return final result
    return num;
}
  
/* Driver code*/
int main()
{
    int res = swapBits(28, 0, 3, 2);
    cout << "Result = " << res;
    return 0;
}

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Output:

 Result = 7

References:
Swapping individual bits with XOR

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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