# Increment a number by one by manipulating the bits

Given a non-negative integer n. The problem is to increment n by 1 by manipulating the bits of n.

Examples :

```Input : 6
Output : 7

Input : 15
Output : 16
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Following are the steps:

1. Get the position of rightmost unset bit of n. Let this position be k.
2. Set the k-th bit of n.
3. Toggle the last k-1 bits of n.
4. Finally, return n.

## C++

 `// C++ implementation to increment a number  ` `// by one by manipulating the bits ` `#include ` `using` `namespace` `std; ` ` `  `// function to find the position ` `// of rightmost set bit ` `int` `getPosOfRightmostSetBit(``int` `n) ` `{ ` `    ``return` `log2(n & -n); ` `} ` ` `  `// function to toggle the last m bits ` `unsigned ``int` `toggleLastKBits(unsigned ``int` `n, ` `                             ``unsigned ``int` `k) ` `{ ` `    ``// calculating a number 'num' having 'm' bits ` `    ``// and all are set ` `    ``unsigned ``int` `num = (1 << k) - 1; ` ` `  `    ``// toggle the last m bits and return the number ` `    ``return` `(n ^ num); ` `} ` ` `  `// function to increment a number by one ` `// by manipulating the bits ` `unsigned ``int` `incrementByOne(unsigned ``int` `n) ` `{ ` `    ``// get position of rightmost unset bit ` `    ``// if all bits of 'n' are set, then the ` `    ``// bit left to the MSB is the rightmost ` `    ``// unset bit ` `    ``int` `k = getPosOfRightmostSetBit(~n); ` ` `  `    ``// kth bit of n is being set by this operation ` `    ``n = ((1 << k) | n); ` ` `  `    ``// from the right toggle all the bits before the ` `    ``// k-th bit ` `    ``if` `(k != 0) ` `        ``n = toggleLastKBits(n, k); ` ` `  `    ``// required number ` `    ``return` `n; ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``unsigned ``int` `n = 15; ` `    ``cout << incrementByOne(n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation to increment a number  ` `// by one by manipulating the bits ` `import` `java.io.*; ` `import` `java.util.*; ` ` `  `class` `GFG { ` `     `  `    ``// function to find the position ` `    ``// of rightmost set bit ` `    ``static` `int` `getPosOfRightmostSetBit(``int` `n) ` `    ``{ ` `        ``return` `(``int``)(Math.log(n & -n) / Math.log(``2``)); ` `    ``} ` `     `  `    ``// function to toggle the last m bits ` `    ``static` `int` `toggleLastKBits( ``int` `n, ``int` `k) ` `    ``{ ` `        ``// calculating a number 'num' having  ` `        ``// 'm' bits and all are set ` `        ``int` `num = (``1` `<< k) - ``1``; ` `     `  `        ``// toggle the last m bits and return  ` `        ``// the number ` `        ``return` `(n ^ num); ` `    ``} ` `     `  `    ``// function to increment a number by one ` `    ``// by manipulating the bits ` `    ``static` `int` `incrementByOne( ``int` `n) ` `    ``{ ` `        ``// get position of rightmost unset bit ` `        ``// if all bits of 'n' are set, then the ` `        ``// bit left to the MSB is the rightmost ` `        ``// unset bit ` `        ``int` `k = getPosOfRightmostSetBit(~n); ` `     `  `        ``// kth bit of n is being set  ` `        ``// by this operation ` `        ``n = ((``1` `<< k) | n); ` `     `  `        ``// from the right toggle all  ` `        ``// the bits before the k-th bit ` `        ``if` `(k != ``0``) ` `            ``n = toggleLastKBits(n, k); ` `     `  `        ``// required number ` `        ``return` `n; ` `     `  `    ``} ` `     `  `    ``// Driver Program     ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `n = ``15``; ` `        ``System.out.println(incrementByOne(n));  ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by Gitanjali. `

## Python 3

 `# python 3 implementation  ` `# to increment a number  ` `# by one by manipulating  ` `# the bits ` `import` `math ` ` `  `# function to find the ` `# position of rightmost  ` `# set bit ` `def` `getPosOfRightmostSetBit(n) : ` `    ``return` `math.log2(n & ``-``n) ` `     `  ` `  `# function to toggle the last m bits ` `def` `toggleLastKBits(n, k) : ` `    ``# calculating a number   ` `    ``# 'num' having 'm' bits  ` `    ``# and all are set ` `    ``num ``=` `(``1` `<< (``int``)(k)) ``-` `1` ` `  `    ``# toggle the last m bits and  ` `    ``# return the number ` `    ``return` `(n ^ num) ` ` `  ` `  `# function to increment  ` `# a number by one by  ` `# manipulating the bits ` `def` `incrementByOne(n) : ` ` `  `    ``# get position of rightmost  ` `    ``# unset bit if all bits of  ` `    ``# 'n' are set, then the bit  ` `    ``# left to the MSB is the  ` `    ``# rightmost unset bit ` `    ``k ``=` `getPosOfRightmostSetBit(~n) ` ` `  `    ``# kth bit of n is being  ` `    ``# set by this operation ` `    ``n ``=` `((``1` `<< (``int``)(k)) | n) ` ` `  `    ``# from the right toggle  ` `    ``# all the bits before the ` `    ``# k-th bit ` `    ``if` `(k !``=` `0``) : ` `        ``n ``=` `toggleLastKBits(n, k) ` ` `  `    ``# required number ` `    ``return` `n ` `     `  `  `  `# Driver program ` `n ``=` `15` `print``(incrementByOne(n)) ` ` `  ` `  `# This code is contributed  ` `# by Nikita Tiwari. `

## C#

 `// C# implementation to increment a number  ` `// by one by manipulating the bits ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// function to find the position ` `    ``// of rightmost set bit ` `    ``static` `int` `getPosOfRightmostSetBit(``int` `n) ` `    ``{ ` `        ``return` `(``int``)(Math.Log(n & -n) / Math.Log(2)); ` `    ``} ` `     `  `    ``// function to toggle the last m bits ` `    ``static` `int` `toggleLastKBits( ``int` `n, ``int` `k) ` `    ``{ ` `         `  `        ``// calculating a number 'num' having  ` `        ``// 'm' bits and all are set ` `        ``int` `num = (1 << k) - 1; ` `     `  `        ``// toggle the last m bits and return  ` `        ``// the number ` `        ``return` `(n ^ num); ` `    ``} ` `     `  `    ``// function to increment a number by one ` `    ``// by manipulating the bits ` `    ``static` `int` `incrementByOne( ``int` `n) ` `    ``{ ` `         `  `        ``// get position of rightmost unset bit ` `        ``// if all bits of 'n' are set, then the ` `        ``// bit left to the MSB is the rightmost ` `        ``// unset bit ` `        ``int` `k = getPosOfRightmostSetBit(~n); ` `     `  `        ``// kth bit of n is being set  ` `        ``// by this operation ` `        ``n = ((1 << k) | n); ` `     `  `        ``// from the right toggle all  ` `        ``// the bits before the k-th bit ` `        ``if` `(k != 0) ` `            ``n = toggleLastKBits(n, k); ` `     `  `        ``// required number ` `        ``return` `n; ` `     `  `    ``} ` `     `  `    ``// Driver Program  ` `    ``public` `static` `void` `Main () ` `    ``{ ` `        ``int` `n = 15; ` `         `  `        ``Console.WriteLine(incrementByOne(n));  ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by Sam007. `

## PHP

 ` `

Output :

```16
```

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