Toggle bits of a number except first and last bits

Last Updated : 3 Aug, 2022

Given a number, the task is to toggle bits of the number except the first and the last bit.
Examples: 

Input : 10
Output : 12
Binary representation:- 1 0 1 0
After toggling first and last : 1 1 0 0

Input : 9
Output : 15
Binary representation : 1 0 0 1
After toggling first and last : 1 1 1 1

Prerequisite: Find most significant set bit of a number

  1. Generate a number that contains the middle bit as a set. We need to change all middle bits to 1 and keep corner bits as 
  2. The answer is XOR of generated number and original number. Note that XOR of 1 with a number toggles the number.
C++ 
// C++ Program to toggle bits 
// except first and last bit
#include<iostream>
using namespace std;

// return set middle bits
int setmiddlebits(int n)
{

    // set all bit
    n |= n >> 1;
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;

    // return middle set bits
    // shift by 1 and xor with 1
    return (n >> 1) ^ 1;
}

int togglemiddlebits(int n)
{
    
    // if number is 1 then
    // simply return
    if (n == 1)
        return 1;

    // xor with
    // middle bits
    return n ^ setmiddlebits(n);
}

// Driver Code
int main()
{
    
    // Given number
    int n = 9;

    // print toggle bits
    cout<<togglemiddlebits(n);

    return 0;
}
Java 
// Java program for toggle bits
// expect first and last bit
import java.io.*;

class GFG {
    
    // return set middle bits
    static int setmiddlebits(int n)
    {

        // set all bit
        n |= n >> 1;
        n |= n >> 2;
        n |= n >> 4;
        n |= n >> 8;
        n |= n >> 16;
    
        // return middle set bits
        // shift by 1 and xor with 1
        return (n >> 1) ^ 1;
    }

    static int togglemiddlebits(int n)
    {
        // if number is 1 then 
        // simply return
        if (n == 1)
            return 1;
    
        // XOR with middle bits
        return n ^ setmiddlebits(n);
    }
    
    // Driver Code
    public static void main (String[] args) 
    {
    
        // Given number
        int n = 9;
    
        // print toggle bits
        System.out.println(togglemiddlebits(n));
    }
}

// This code is contributed by vt_m
Python3 
# Python3 program for toggle bits
# expect first and last bit

# return set middle bits
def setmiddlebits(n):

    # set all bit
    n |= n >> 1;
    n |= n >> 2;
    n |= n >> 4;
    n |= n >> 8;
    n |= n >> 16;

    # return middle set bits
    # shift by 1 and xor with 1
    return (n >> 1) ^ 1

def togglemiddlebits(n):

    # if number is 1 then simply return
    if (n == 1):
        return 1

    # xor with middle bits
    return n ^ setmiddlebits(n)

# Driver code
n = 9
print(togglemiddlebits(n))

# This code is contributed by Anant Agarwal.
C# 
// C# program for toggle bits
// expect first and last bit
using System;

class GFG {
    
    // return set middle bits
    static int setmiddlebits(int n)
    {

        // set all bit
        n |= n >> 1;
        n |= n >> 2;
        n |= n >> 4;
        n |= n >> 8;
        n |= n >> 16;
        
        // return middle set bits
        // shift by 1 and xor with 1
        return (n >> 1) ^ 1;
    }

    static int togglemiddlebits(int n)
    {
        
        // if number is 1 then 
        // simply return
        if (n == 1)
            return 1;
    
        // XOR with middle bits
        return n ^ setmiddlebits(n);
    }
    
    // Driver Code
    public static void Main ()
    {
    
        // Given number
        int n = 9;
    
        // print toggle bits
        Console.WriteLine(togglemiddlebits(n));
    }
}

// This code is contributed by Anant Agarwal.
PHP 
<?php
// Php Program to toggle bits 
// except first and last bit

// return set middle bits
function setmiddlebits($n)
{

    // set all bit
    $n |= $n >> 1;
    $n |= $n >> 2;
    $n |= $n >> 4;
    $n |= $n >> 8;
    $n |= $n >> 16;

    // return middle set bits
    // shift by 1 and xor with 1
    return ($n >> 1) ^ 1;
}

function togglemiddlebits($n)
{
    
    // if number is 1 then
    // simply return
    if ($n == 1)
        return 1;

    // xor with
    // middle bits
    return $n ^ setmiddlebits($n);
}

    // Driver Code
    $n = 9;

    // print toggle bits
    echo togglemiddlebits($n);

// This code is contributed by ajit
?>
JavaScript 
<script>

// Javascript Program to toggle bits 
// except first and last bit 

// return set middle bits 
function setmiddlebits(n) 
{ 

    // set all bit 
    n |= n >> 1; 
    n |= n >> 2; 
    n |= n >> 4; 
    n |= n >> 8; 
    n |= n >> 16; 

    // return middle set bits 
    // shift by 1 and xor with 1 
    return (n >> 1) ^ 1; 
} 

function togglemiddlebits(n) 
{ 
    
    // if number is 1 then 
    // simply return 
    if (n == 1) 
        return 1; 

    // xor with 
    // middle bits 
    return n ^ setmiddlebits(n); 
} 

// Driver Code 

// Given number 
var n = 9; 
// print toggle bits 
document.write(togglemiddlebits(n));
    
</script>

Output
15

Time Complexity: O(log2n), where n is the given number 
Auxiliary Space: O(1)
 

Another Approach: Using bit mask
The idea to solve this problem is that we can use XOR of a specific bit with 1 to toggle the specific bit. Therefore, for an n - bit number, we can construct a bit mask of the form 0111....11110, ie, an n - bit number, where all bits are set except the first and last bit. Therefore, for a number that is greater than or equal to 4, the bit mask is equal to 2n - 2. (n can be calculated using log2number)  (For numbers less than 4, there are no middle bits, therefore, the number will not be changed).

Approach:

  1. Calculate the bit mask = 2 log2number - 2
  2. Perform the XOR of the number and the mask.

Below is the implementation of the above approach:

C++ 
// C++ Program to toggle bits 
// except first and last bit
#include<bits/stdc++.h>
using namespace std;


//function to toggle the middle bits
//using the bit mask
int togglemiddlebits(int n)
{
    //if n < 4, there are no middle bits
    if (n < 4)
        return n;
    int mask = (1 << (int)log2(n)) - 2;
    return mask ^ n;
}

// Driver Code
int main()
{
    
    // Given number
    int n = 9;
    
    //Function call
    cout << togglemiddlebits(n) << endl;

    return 0;
}

//This code is contributed by phasing17
Java 
// Java Program to toggle bits 
// except first and last bit
import java.io.*;
import java.util.*; 

class GFG
{

  // function to toggle the middle bits
  // using the bit mask    
  public static int togglemiddlebits(int n)
  {

    // if n < 4, there are no middle bits
    if (n < 4)
      return n;
    int mask = (1 << (int)(Math.log(n) / Math.log(2))) - 2;
    return mask ^ n;
  }    

  // Driver Code
  public static void main(String[] args)
  {

    // Given number
    int n = 9;

    //Function call
    System.out.println(togglemiddlebits(n));
  }
}

// this code is contributed by adityapatil12
Python3 
# python3 Program to toggle bits 
# except first and last bit

import math  
#function to toggle the middle bits
#using the bit mask
def togglemiddlebits(n) :
    
    #if n < 4, there are no middle bits
    if n < 4 :
        return n
    mask = int((1 << int(math.log2(14))) - 2)
    return mask ^ n
    
# Driver code
if __name__ == "__main__" :
    
    # Given number
    n = 9
    
    # Function call
    print(togglemiddlebits(n))

# this code is contributed by aditya942003patil
C# 
// C# Program to toggle bits
// except first and last bit

using System;

class GFG {

  // function to toggle the middle bits
  // using the bit mask
  static int togglemiddlebits(int n)
  {
    // if n < 4, there are no middle bits
    if (n < 4)
      return n;
    int mask
      = (1 << (int)(Math.Log(n) / Math.Log(2))) - 2;
    return mask ^ n;
  }

  // Driver Code
  public static void Main(string[] args)
  {

    // Given number
    int n = 9;

    // Function call
    Console.WriteLine(togglemiddlebits(n));
  }
}

// This code is contributed by phasing17
JavaScript 
// JavaScript Program to toggle bits 
// except first and last bit


//Function to toggle the middle bits
//using the bit mask
function togglemiddlebits(n)
{

    //if n < 4, there are no middle bits
    if (n < 4)
        return n;
    let mask = (1 << Math.floor(Math.log2(n))) - 2;
    return mask ^ n;
}

// Driver Code
// Given number
let n = 9;
    
//Function call
console.log(togglemiddlebits(n));


//This code is contributed by phasing17

Output
15

Time Complexity: O(1)
Auxiliary Space: O(1)

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Article Tags:
Misc
Bit Magic
DSA

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