Add two bit strings (original) (raw)

Last Updated : 26 Apr, 2025

Given two binary strings s1 and **s2 consisting of only 0s and 1s. Find the resultant string after adding the two Binary Strings.
**Note: The input strings may contain leading zeros but the output string should not have any leading zeros.

**Examples:

**Input: s1 = "1101", s2 = "111"
**Output: 10100
**Explanation: "1101" and "111" in decimal representation will be 13 and 7 respectively. Adding both the numbers gives 20, and its binary representation is "10100".

**Input: s1 = "00100", s2 = "010"
**Output: 110
**Explanation: "00100" and "010" in decimal representation will be 4 and 2 respectively. Adding both the numbers gives 6, and its binary representation is "110".

This problem can be solved using Bit-by-bit addition with carry in O(n + m) Time and O(1) Space, The idea is to first trim the leading zeros in the input strings. Now, start from the **last characters of the strings and compute the digit sum one by one. If the **sum becomes more than **1, then store **carry for the next digits. Also consider this **carry while calculating the digit sum. After calculating the sum, if an additional carry is generated, prepend a ‘1’ of the **result.

Please refer Add two binary strings for detailed explanation and solution.

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