addBits.js

function addBits(v1, v2) {
  const toNumberArray = str => str.split("").map(_ => +_);
  const [a1, a2] = [toNumberArray(v1), toNumberArray(v2)];

  // Add bits from right (least significant bit)
  // to left (most significant bit)
  const sum = a1.reduceRight((acc, a, i) => {
    const b = a2[i];
    // c => carry, s => sum
    let [c, s] = [0, 0];

    // Calculate the first bit
    if (i === a1.length - 1) {
      ({ c, s } = halfAdder(a, b));
    } else {
      // Calculate the rest of the bits using the carry
      const carry = (acc[0] && acc[0].c) || 0;
      ({ c, s } = fullAdder(a, b, carry));
    }

    return [{ c, s }, ...acc];
  }, []);

  // Build readable text
  return sum.reduce(
    (acc, { s, c }, i) => `${acc}${(i === 0 && c === 1 && "1") || ""}${s}`,
    ""
  );
}