# Binary representation of next number

Given a binary input that represents binary representation of positive number n, find binary representation of n+1.

The binary input may be and may not fit even in unsigned long long int.

Examples:

```Input : 10011
Output : 10100
Here n = (19)10 = (10011)2
next greater integer = (20)10 = (10100)2

Input : 111011101001111111
Output : 111011101010000000
```

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

We store input as string so that large numbers can be handled. We traverse the string from rightmost character and convert all 1s to 0s until we find a 0. Finally convert the found 0 to 1. If we do not find a 0, we append a 1 to overall string.

```string nextGreater(num)
l = num.length

// Find first 0 from right side. While
// searching, convert 1s to 0s
for i = l-1 to 0
if num[i] == '0'
num[i] = '1'
break
else
num[i] = '0'

// If there was no 0
if i < 0
num = '1' + num
return num
```

Below is C++ implementation of above idea.

```// C++ implementation to find the binary
// representation of next greater integer
#include <bits/stdc++.h>
using namespace std;

// function to find the required
// binary representation
string nextGreater(string num)
{
int l = num.size();

// examine bits from the right
for (int i=l-1; i>=0; i--)
{
// if '0' is encountered, convert
// it to '1' and then break
if (num.at(i) == '0')
{
num.at(i) = '1';
break;
}

// else convert '1' to '0'
else
num.at(i) = '0';
}

// if the binary representation
// contains only the set bits
if (i < 0)
num = "1" + num;

// final binary representation
// of the required integer
return num;
}

// Driver program to test above
int main()
{
string num = "10011";
cout << "Binary representation of next number = "
<< nextGreater(num);
return 0;
}```

Output:

```Binary representation of next number = 10100
```

Time Complexity : O(n) where n is number of bits in input.

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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