BigInt String Arithmetic

Arbitrary-precision arithmetic adds and multiplies numbers that are too large to fit in a machine word by operating on their decimal digits directly, exactly the way you would on paper. JavaScript's number type is an IEEE-754 double that stays exact only up to Number.MAX_SAFE_INTEGER (that is 2^53 - 1, or 9007199254740991); past that, calling Number('12345678901234567890') silently rounds the value before you have done any math. You will implement add and multiply for non-negative integers handed to you as decimal strings of any length, packaged on one object bigintStringArithmetic = { add, multiply } — no BigInt, no Number on the whole value, no libraries.

Signature

bigintStringArithmetic.add(a, b)       // (decimal string, decimal string) -> decimal string
bigintStringArithmetic.multiply(a, b)  // (decimal string, decimal string) -> decimal string

Examples

bigintStringArithmetic.add('2', '3');   // '5'
bigintStringArithmetic.add('99', '1');  // '100'
bigintStringArithmetic.add('12345678901234567890', '98765432109876543210');
// '111111111011111111100'  — a plain Number(a) + Number(b) drops the low digits

bigintStringArithmetic.multiply('123', '456');  // '56088'
bigintStringArithmetic.multiply('99', '99');    // '9801'
bigintStringArithmetic.multiply('12345678901234567890', '0');  // '0'

Notes

• Inputs are canonical — each argument is a non-negative integer with no sign and no leading zeros, except '0' itself, which is exactly one zero. You do not need to validate them.
• No shortcuts — you may not use BigInt, convert the whole string with Number or parseInt, or reach for a big-number library. Converting a single digit character is fine; converting the whole value is the bug.
• Return a canonical string — strip any leading zeros so multiply('0', '5') returns '0', not '000', and add('1', '9') returns '10'.
• Any length — inputs can be hundreds of digits long, so your solution must work digit by digit rather than lean on machine-word size.
• Non-negative only — no subtraction, no negatives, no decimal points. Just addition and multiplication of whole numbers.