This implements big integer addition in a naive way

naive_bigint_impl.js

let x = '12345678901234567890';
let y = '12345678901234567890';

let maxLen = Math.max(x.length, y.length)
if (maxLen !== x.length) {
	let tempX = y;
	y = x;
	x = tempX;
}

if (x.length !== y.length) {
	let padLen = x.length - y.length;
	let zeros = '';
	for (let i = 0; i < padLen; i++) {
		zeros += 0;
	}
	y = zeros + y;
}

let arr = [];
let carry = 0;
for (let i = x.length - 1; i >= 0; i--) {
	let sum = Number(x[i]) + Number(y[i]) + carry;
	carry = Math.floor(sum / 10);
	arr.push(sum > 9 ? sum - 10 : sum);
}

if (carry !== 0) {
	arr.push(carry);
}

let res = '';
for (let i = arr.length - 1; i >= 0; i--) {
	res += String(arr[i]);
}

console.log(res);