Add Two Binary Digit Strings
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
The strings `first` and `second` represent nonnegative integers in base two. Return their sum as a binary digit string, using the usual representation without unnecessary leading zeroes.
### Examples
**Example 1**
```text
Input: first = "1101", second = "101"
Output: "10010"
```
The represented values are `13` and `5`; their sum, `18`, is written as `10010` in binary.
**Example 2**
```text
Input: first = "0", second = "1001"
Output: "1001"
```
Adding zero preserves the other value.
### Constraints
- Each input string has length between `1` and `10^4`, inclusive.
- The only permitted characters are `0` and `1`.
- Each input has no leading zeroes unless the entire string is `"0"`.
Overview: Add two canonical binary digit strings and return their exact sum in binary, including zero and long input representations.