Your Scientific Calculator Handles Signed Arbitrary-Precision Addition Including Negatives

Technical Interview Challenge: The "Signed Ledger" Arithmetic Engine

Context

In advanced financial engineering and scientific computing, precision is non-negotiable. Standard JavaScript numbers use the IEEE 754 format, which loses integer precision beyond $2^{53} - 1$. While unsigned "Big Addition" is a common problem, real-world systems must handle signed arithmetic—processing both credits (positive) and debits (negative) of arbitrary magnitude.

You are building the core arithmetic module for a high-precision calculator. This module must handle the mathematical signs manually, effectively simulating how a CPU performs arithmetic at the bit level, but using decimal strings.

Problem Statement

Implement a function bigAddSigned(a, b) that takes two strings representing signed integers and returns their sum as a string.

Requirements:

1. Sign Handling: Correctly process inputs that are positive (e.g., "123"), negative (e.g., "-456"), or zero ("0").

2. No Native BigInt: You are strictly forbidden from using the BigInt constructor or BigInt literals.

3. Arbitrary Precision: The strings may contain hundreds of digits, far exceeding the limits of the Number type.

4. Mathematical Correctness:

   • Adding two negatives: (-A) + (-B) = -(A + B)

   • Adding a positive and a negative: A + (-B) = A - B

5. Clean Output: Resulting strings should not have unnecessary leading zeros (e.g., return "0", not "-0" or "007").

Example Use Cases

Example 1: Opposite Signs (Subtraction Logic)

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Example 2: Both Negative (Addition Logic)

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Example 3: Zero Result

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Example 4: Large Magnitude

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Interview Evaluation Criteria

• Algorithm Selection: How do you decide between using a "Big Addition" helper versus a "Big Subtraction" helper?

• Magnitude Comparison: To compute $A - B$ where $B > A$, you must recognize that the result will be $-(B - A)$. How do you efficiently compare the magnitude of two numeric strings?

• Edge Case Management: How do you handle cases where the result is 0 or when one input has a sign and the other does not?

• Modular Code: Do you break the problem into smaller, reusable pieces (e.g., compare(a, b), add(a, b), and subtract(a, b))?