Binary Addition of Strings | Dataford Interview Questions

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Problem

Oscar Health's member eligibility workflow may represent compact flags or counters as binary strings. Implement binary addition for two non-negative binary strings without converting either input to a built-in integer type.

Return the binary representation of their sum without leading zeros, except that the result for zero must be "0".

Formal Specification

Implement add_binary(a, b):

Input: two strings a and b, each containing only the characters 0 and 1.
Output: a string containing only 0 and 1, representing the exact sum of the two inputs in base two.
Do not use integer parsing, arbitrary-precision conversion, or floating-point arithmetic to convert the complete input strings.

Process digits from right to left, maintaining a carry just as in decimal addition. The inputs may have different lengths and may contain leading zeros.

Constraints

1 <= len(a), len(b) <= 10^5
Each input contains only the characters 0 and 1.
Inputs may contain leading zeros.
The result must not contain leading zeros unless it is exactly "0".

Function Signature

def add_binary(a, b):