# Toggle all bits after most significant bit

• Difficulty Level : Hard
• Last Updated : 14 Jul, 2022

Given a number, toggle all bits of it after most significant bit including most significant bit.

Examples :

```Input : 10
Output : 5
Binary representation of 10 is 1010
After toggling we get 0101

Input : 5
Output : 2```

We can toggle a bit by doing XOR of it with 1 (Note that 1 ^ 0 = 1 and 1 ^ 1 = 0). The idea is to take a number temp with only one bit set. One by one move the only set bit of temp to left and do XOR of it with n until it crosses MSB (Most Significant Bit) of n.

## C++

 `// CPP program to toggle set  bits starting``// from MSB``#include``using` `namespace` `std;` `void` `toggle(``int` `&n)``{``    ``// temporary variable to``    ``// use XOR with one of a n``    ``int` `temp = 1;` `    ``// Run loop until the only``    ``// set bit in temp crosses``    ``// MST of n.``    ``while` `(temp <= n)``    ``{``        ``// Toggle bit of n``        ``// corresponding to``        ``// current set bit in``        ``// temp.``        ``n = n ^ temp;` `        ``// Move set bit to next``        ``// higher position.``        ``temp = temp << 1;``    ``}``}` `// Driver code``int` `main()``{``    ``int` `n = 10;``    ``toggle(n);``    ``cout << n;``    ``return` `0;``}`

## Java

 `// Java program to toggle set``// bits starting from MSB` `class` `GFG {``    ` `static` `int` `toggle(``int` `n) {``    ` `    ``// temporary variable to``    ``// use XOR with one of a n``    ``int` `temp = ``1``;` `    ``// Run loop until the only``    ``// set bit in temp crosses``    ``// MST of n.``    ``while` `(temp <= n) {``        ` `    ``// Toggle bit of n``    ``// corresponding to``    ``// current set bit in``    ``// temp.``    ``n = n ^ temp;` `    ``// Move set bit to next``    ``// higher position.``    ``temp = temp << ``1``;``    ``}``    ``return` `n;``}` `// Driver code``public` `static` `void` `main(String arg[])``{``    ``int` `n = ``10``;``    ``n = toggle(n);``    ``System.out.print(n);``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python program to toggle``# set  bits starting``# from MSB` `def` `toggle(n):` `    ``# temporary variable to``    ``# use XOR with one of a n``    ``temp ``=` `1`` ` `    ``#Run loop until the only``    ``#set bit in temp crosses``    ``#MST of n.``    ``while` `(temp <``=` `n):``    ` `        ``# Toggle bit of n``        ``# corresponding to``        ``# current set bit in``        ``# temp.``        ``n ``=` `n ^ temp`` ` `        ``# Move set bit to next``        ``# higher position.``        ``temp ``=` `temp << ``1` `    ``return` `n`` ` `# Driver code` `n ``=` `10``n``=``toggle(n)``print``(n)` `# This code is contributed``# by Anant Agarwal.`

## C#

 `// C# program to toggle set``// bits starting from MSB``using` `System;` `class` `GFG {` `// Function to toggle bits``// starting from MSB   ``static` `int` `toggle(``int` `n) {``    ` `    ``// temporary variable to``    ``// use XOR with one of a n``    ``int` `temp = 1;` `    ``// Run loop until the only``    ``// set bit in temp crosses``    ``// MST of n.``    ``while` `(temp <= n) {``        ` `    ``// Toggle bit of n``    ``// corresponding to``    ``// current set bit in``    ``// temp.``    ``n = n ^ temp;` `    ``// Move set bit to next``    ``// higher position.``    ``temp = temp << 1;``    ``}``    ``return` `n;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `n = 10;``    ``n = toggle(n);``    ``Console.Write(n);``}``}` `// This code is contributed by Nitin Mittal.`

## PHP

 ``

## Javascript

 ``

Output

`5`

Time Complexity: O(log n)

Auxiliary Space: O(1)

The above solution can be optimized to work in O(1) time under the assumption that numbers are stored in 32 bits.

## C++

 `// CPP program to toggle set  bits starting``// from MSB``#include``using` `namespace` `std;` `// Returns a number which has all set bits``// starting from MSB of n``int` `setAllBitsAfterMSB(``int` `n)``{   ``    ``// This makes sure two bits``    ``// (From MSB and including MSB)``    ``// are set``    ``n |= n>>1;` `    ``// This makes sure 4 bits``    ``// (From MSB and including MSB)``    ``// are set``    ``n |= n>>2;  ` `    ``n |= n>>4; ``    ``n |= n>>8;``    ``n |= n>>16;``    ``return` `n;``}` `void` `toggle(``int` `&n)``{``    ``n = n ^ setAllBitsAfterMSB(n);``}` `// Driver code``int` `main()``{``    ``int` `n = 10;``    ``toggle(n);``    ``cout << n;``    ``return` `0;``}`

## Java

 `// Java program to toggle set bits``// starting from MSB` `class` `GFG {``    ` `// Returns a number which has all``// set bits starting from MSB of n``static` `int` `setAllBitsAfterMSB(``int` `n) {``    ` `    ``// This makes sure two bits``    ``// (From MSB and including MSB)``    ``// are set``    ``n |= n >> ``1``;` `    ``// This makes sure 4 bits``    ``// (From MSB and including MSB)``    ``// are set``    ``n |= n >> ``2``;` `    ``n |= n >> ``4``;``    ``n |= n >> ``8``;``    ``n |= n >> ``16``;``    ``return` `n;``}``static` `int` `toggle(``int` `n)``{``    ``n = n ^ setAllBitsAfterMSB(n);``    ``return` `n;``}` `// Driver code``public` `static` `void` `main(String arg[])``{``    ``int` `n = ``10``;``    ``n = toggle(n);``    ``System.out.print(n);``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python program to toggle set  bits starting``# from MSB` `# Returns a number which has all set bits``# starting from MSB of n``def` `setAllBitsAfterMSB(n):`` ` `    ``# This makes sure two bits``    ``# (From MSB and including MSB)``    ``# are set``    ``n |``=` `n>>``1`` ` `    ``# This makes sure 4 bits``    ``# (From MSB and including MSB)``    ``# are set``    ``n |``=` `n>>``2`  ` ` `    ``n |``=` `n>>``4` `    ``n |``=` `n>>``8``    ``n |``=` `n>>``16``    ``return` `n` `def` `toggle(n):` `    ``n ``=` `n ^ setAllBitsAfterMSB(n)``    ``return` `n``    ` `#Driver code` `n ``=` `10``n``=``toggle(n)``print``(n)``# This code is contributed by Anant Agarwal.`

## C#

 `// C# program to toggle set bits``// starting from MSB``using` `System;` `class` `GFG {``        ` `    ``// Returns a number which has all``    ``// set bits starting from MSB of n``    ``static` `int` `setAllBitsAfterMSB(``int` `n)``    ``{``        ` `        ``// This makes sure two bits``        ``// (From MSB and including MSB)``        ``// are set``        ``n |= n >> 1;``    ` `        ``// This makes sure 4 bits``        ``// (From MSB and including MSB)``        ``// are set``        ``n |= n >> 2;``    ` `        ``n |= n >> 4;``        ``n |= n >> 8;``        ``n |= n >> 16;``        ``return` `n;``    ``}``    ` `    ``static` `int` `toggle(``int` `n)``    ``{``        ``n = n ^ setAllBitsAfterMSB(n);``        ``return` `n;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 10;``        ``n = toggle(n);``        ``Console.WriteLine(n);``    ``}``}` `// This code is contributed by Sam007.`

## PHP

 `> 1;` `    ``// This makes sure 4 bits``    ``// (From MSB and including MSB)``    ``// are set``    ``\$n` `|= ``\$n` `>> 2;` `    ``\$n` `|= ``\$n` `>> 4;``    ``\$n` `|= ``\$n` `>> 8;``    ``\$n` `|= ``\$n` `>> 16;``    ``return` `\$n``;``}``function` `toggle(&``\$n``)``{``    ``\$n` `= ``\$n` `^ setAllBitsAfterMSB(``\$n``);``}` `// Driver Code``\$n` `= 10;``toggle(``\$n``);``echo` `\$n``;` `// This code is contributed by ajit``?>`

## Javascript

 ``

Output

`5`

Time Complexity: O(1)

Auxiliary Space: O(1)

Thanks to Devanshu Agarwal for suggesting this approach.

Another Approach:

To toggle a specific bit, we can take XOR of that bit with 1.

Therefore, for an n – bit number, we can construct a binary mask of the form 1111….11111, ie, all n bits are set. This is nothing but 2n – 1.

The implementation is shown below:

## C++

 `// CPP program to toggle set  bits starting``// from MSB``#include``using` `namespace` `std;` `// Returns a number which has all set bits``// starting from MSB of n``int` `toggle(``int` `num)``{  ``    ``//the number of bits is equal to log2num + 1``    ``int` `n = (``int``)log2(num) + 1;``    ``//calculating mask``    ``int` `mask = ``pow``(2, n) - 1;``    ``//toggling bits using xor with mask``    ``return` `num ^ mask;``}`  `// Driver code``int` `main()``{``    ``int` `num = 10;``    ``cout << toggle(num);``}` `//this code is contributed by phasing17`

## Java

 `// Java program to toggle set  bits starting``// from MSB``import` `java.util.*;` `class` `GFG {` `  ``// Returns a number which has all set bits``  ``// starting from MSB of n``  ``static` `int` `toggle(``int` `num)``  ``{``    ``// the number of bits is equal to log2num + 1``    ``int` `n = (``int``)(Math.log(num) / Math.log(``2``)) + ``1``;` `    ``// calculating mask``    ``int` `mask = (``int``)Math.pow(``2``, n) - ``1``;` `    ``// toggling bits using xor with mask``    ``return` `num ^ mask;``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String[] args)``  ``{``    ``int` `num = ``10``;``    ``System.out.println(toggle(num));``  ``}``}` `// this code is contributed by phasing17`

## Python3

 `# Python3 program to toggle set``# bits starting from MSB``from` `math ``import` `log` `# Returns a number which has all set bits``# starting from MSB of n``def` `toggle(num):` `    ``# the number of bits is equal to log2num + 1``    ``n ``=` `int``(log(num, ``2``)) ``+` `1` `    ``# calculating mask``    ``mask ``=` `pow``(``2``, n) ``-` `1` `    ``# toggling bits using xor with mask``    ``return` `num ^ mask` `# Driver code``num ``=` `10``print``(toggle(num))` `# This code is contributed by phasing17`

## C#

 `// C# program to toggle set  bits starting``// from MSB``using` `System;` `class` `GFG {` `  ``// Returns a number which has all set bits``  ``// starting from MSB of n``  ``static` `int` `toggle(``int` `num)``  ``{``    ` `    ``// the number of bits is equal to log2num + 1``    ``int` `n = (``int``)(Math.Log(num) / Math.Log(2)) + 1;` `    ``// calculating mask``    ``int` `mask = (``int``)Math.Pow(2, n) - 1;` `    ``// toggling bits using xor with mask``    ``return` `num ^ mask;``  ``}` `  ``// Driver code``  ``public` `static` `void` `Main(``string``[] args)``  ``{``    ``int` `num = 10;``    ``Console.WriteLine(toggle(num));``  ``}``}` `// This code is contributed by phasing17`

## Javascript

 `// JavaScript program to toggle set``// bits starting from MSB` `// Returns a number which has all set bits``// starting from MSB of n``function` `toggle(num)``{  ``    ``// the number of bits is equal to log2num + 1``    ``let n = Math.floor((Math.log(num) / Math.log(2)) + 1);``    ` `    ``// calculating mask``    ``let mask = Math.pow(2, n) - 1;``    ` `    ``// toggling bits using xor with mask``    ``return` `num ^ mask;``}` `// Driver code``let num = 10;``console.log(toggle(num));` `// this code is contributed by phasing17`

Output

`5`

Time Complexity: O(logn)

Auxiliary Space: O(1)

This article is contributed by Devanshu Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes arrow_drop_up