## Related Articles

• Write an Interview Experience
• String Data Structure

• Difficulty Level : Medium
• Last Updated : 28 Jun, 2022

Given two bit sequences as strings, write a function to return the addition of the two sequences. Bit strings can be of different lengths also. For example, if string 1 is “1100011” and second string 2 is “10”, then the function should return “1100101”.

## We strongly recommend that you click here and practice it, before moving on to the solution.

Since the sizes of two strings may be different, we first make the size of a smaller string equal to that of the bigger string by adding leading 0s. After making sizes the same, we one by one add bits from rightmost bit to leftmost bit. In every iteration, we need to sum 3 bits: 2 bits of 2 given strings and carry. The sum bit will be 1 if, either all of the 3 bits are set or one of them is set. So we can do XOR of all bits to find the sum bit. How to find carry – carry will be 1 if any of the two bits is set. So we can find carry by taking OR of all pairs. Following is step by step algorithm.
1. Make them equal sized by adding 0s at the beginning of smaller string.
…..Boolean expression for adding 3 bits a, b, c
…..Sum = a XOR b XOR c
…..Carry = (a AND b) OR ( b AND c ) OR ( c AND a )
Following is implementation of the above algorithm.

## Python3

 # Python3 program for above approach # adds the two-bit strings and return the result # Helper method: given two unequal sized bit strings,# converts them to same length by adding leading 0s# in the smaller string. Returns the new lengthdef makeEqualLength(str1, str2):     len1 = len(str1)     # Length of string 1    len2 = len(str2)     # length of string 2    if len1 < len2:        str1 = (len2 - len1) * '0' + str1        len1 = len2    elif len2 < len1:        str2 = (len1 - len2) * '0' + str2        len2 = len1    return len1, str1, str2 def addBitStrings( first, second ):    result = '' # To store the sum bits     # make the lengths same before adding    length, first, second = makeEqualLength(first, second)     carry = 0 # initialize carry as 0     # Add all bits one by one    for i in range(length - 1, -1, -1):        firstBit = int(first[i])        secondBit = int(second[i])         # boolean expression for sum of 3 bits        sum = (firstBit ^ secondBit ^ carry) + 48        result = chr(sum) + result         # boolean expression for 3 bits addition        carry = (firstBit & secondBit) | \                (secondBit & carry) | \                (firstBit & carry)         # if overflow, then add a leading 1    if carry == 1:        result = '1' + result    return result # Driver Codeif __name__ == '__main__':    str1 = '1100011'    str2 = '10'    print('Sum is', addBitStrings(str1, str2))     # This code is contributed by# chaudhary_19 (Mayank Chaudhary)

## Javascript

Output

Sum is 1100101

Time Complexity: O(|str1|)

Auxiliary Space: O(1)

Method – 2 (without adding extra zeros(0) in beginning of a small length string to make both strings with same length)

Algo :

1. make to pointer i,j and set i = str1.size() – 1 and j = str2.size() – 1
2. take initial carry as 0 ans ans string as empty (“”)
3. while i>=0 or j>=0 or carry
1. add value of str1[i] and str2[j] in carry
3. set carry = carry/2
4. return ans

## C++

 #include using namespace std; // The function that adds two-bit sequences and returns the additionstring addBitStrings(string str1, string str2){    string ans = "";    int i = str1.size() - 1;    int j = str2.size() - 1;    int carry = 0;    while (i >= 0 || j >= 0 || carry) {        carry += ((i >= 0) ? (str1[i--] - '0') : (0));        carry += ((j >= 0) ? (str2[j--] - '0') : (0));        ans = char('0' + (carry % 2)) + ans;        carry = carry / 2;    }    return ans;} // Driver program to test above functionsint main(){    string str1 = "1100011";    string str2 = "10";     cout << "Sum is " << addBitStrings(str1, str2);    return 0;}

## Java

 // Java implementationclass GFG {   // The main function that adds two-bit  // sequences and returns the addition  static String addBitStrings(StringBuilder str1,                              StringBuilder str2)  {    StringBuilder ans = new StringBuilder();    int i = str1.length() - 1;    int j = str2.length() - 1;    int carry = 0;    while (i >= 0 || j >= 0 || carry>0) {      if (i >= 0)        carry += str1.charAt(i--) - '0';      if (j >= 0)        carry += str2.charAt(j--) - '0';      ans.append(carry % 2);      carry = carry/2;    }    return ans.reverse().toString();  }   // Driver Code  public static void main(String[] args)  {    String str1 = "1100011";    String str2 = "10";    System.out.println("Sum is "+ addBitStrings(new StringBuilder(str1),                                                new StringBuilder(str2)));  }} // This code is contributed by ajaymakvana

## Python3

 # The function that adds two-bit sequences and returns the additiondef addBitStrings(str1, str2):    ans = ''    i = len(str1) - 1    j = len(str2) - 1    carry = 0    while i >= 0 or j >= 0 or carry:        if i >= 0:            carry += ord(str1[i]) - ord('0')            i = i - 1        else:            carry += 0         if j >= 0:            carry += ord(str2[j]) - ord('0')            j = j - 1        else:            carry += 0         ans = chr(ord('0') + carry % 2) + ans        carry = carry // 2    return ans  # Driver program to test above functionsstr1 = '1100011'str2 = '10' print('Sum is ', addBitStrings(str1, str2)) # This code is contributed by ajaymakavan.

## C#

 // C# code to implement the approachusing System; public static class Globals{       // The function that adds two-bit sequences and returns    // the addition    public static string addBitStrings(string str1,                                       string str2)    {        string ans = "";        int i = str1.Length - 1;        int j = str2.Length - 1;        int carry = 0;        while (i >= 0 || j >= 0 || carry != 0) {            carry += ((i >= 0) ? (str1[i--] - '0') : (0));            carry += ((j >= 0) ? (str2[j--] - '0') : (0));            ans = (char)('0' + (carry % 2)) + ans;            carry = carry / 2;        }        return ans;    }     // Driver program to test above functions    public static void Main()    {        string str1 = "1100011";        string str2 = "10";         Console.Write("Sum is ");        Console.Write(addBitStrings(str1, str2));    }} // This code is contributed by Aarti_Rathi

## Javascript

 // JavaScript code to implement the approach // The function that adds two-bit sequences and returns the additionfunction addBitStrings(str1, str2){    let ans = "";    let i = str1.length - 1;    let j = str2.length - 1;    let carry = 0;    while (i >= 0 || j >= 0 || (carry != 0)) {        carry += ((i >= 0) ? (parseInt(str1[i--])) : (0));        carry += ((j >= 0) ? (parseInt(str2[j--])) : (0));        ans = (carry % 2).toString() + ans;        carry = Math.floor(carry / 2);    }    return ans;} // Driver program to test above functionslet str1 = "1100011";let str2 = "10"; // Function Callconsole.log("Sum is", addBitStrings(str1, str2)); // This code is contributed by phasing17

Output

Sum is 1100101
Time Complexity: O(max(n,m)) (where, n = sizeof str1 & m = sizeof str2)
Space Complexity: O(1)