Given two binary strings a and b, return their sum, also as a binary string. This is elementary-school addition, just in base 2 instead of base 10 — walk both strings from the rightmost digit, add corresponding digits plus any carry from the previous position, and keep the overflow as a carry into the next position. The only real design decision is HOW to build the result string as you go: strings are immutable, so repeatedly gluing a new digit onto the FRONT forces a full copy every time. Appending to the end instead — then reversing once at the finish — does the same amount of real work in a fraction of the total time.