Toggle bits of a number except first and last bits

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

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
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

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:

Calculate the bit mask = 2^log_²^number – 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