Sum of Two Integers — Step-by-Step Visualization

Algorithm Pattern

Bit Manipulation (XOR + Carry)

Key Idea

XOR gives the sum of bits without carry. AND shifted left gives the carry. Repeat until carry is zero.

Step-by-Step Approach

1. Compute carry = (a & b) << 1.
2. Compute partial sum a = a ^ b.
3. Set b = carry.
4. Repeat while b != 0.
5. Return a (no remaining carry).

Common Gotchas

• In Python, integers are unbounded — a 32-bit mask is needed to handle negatives.
• In JS, bitwise ops already operate on 32-bit signed integers.