# Program to add two binary strings

Given two binary strings, return their sum (also a binary string).

Example:

```Input:  a = "11", b = "1"
Output: "100"
```

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The idea is to start from last characters of two strings and compute digit sum one by one. If sum becomes more than 1, then store carry for next digits.

```// C++ program to add two binary strings
#include<bits/stdc++.h>
using namespace std;

// This function adds two binary strings and return
// result as a third string
{
string result = ""; // Initialize result
int s = 0;          // Initialize digit sum

// Travers both strings starting from last
// characters
int i = a.size() - 1, j = b.size() - 1;
while (i >= 0 || j >= 0 || s == 1)
{
// Comput sum of last digits and carry
s += ((i >= 0)? a[i] - '0': 0);
s += ((j >= 0)? b[j] - '0': 0);

// If current digit sum is 1 or 3, add 1 to result
result = char(s % 2 + '0') + result;

// Compute carry
s /= 2;

// Move to next digits
i--; j--;
}
return result;
}

// Driver program
int main()
{
string a = "1101", b="100";
cout << addBinary(a, b) << endl;
return 0;
}
```

Output:

`10001`

Thanks to Gaurav Ahirwar for suggesting above solution. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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