Add Without Plus: Arithmetic Addition via Bitwise XOR and AND (CTCI 17.1)

TL;DR

• The Problem: CTCI problem 17.1 technical mechanics.
• The Approach: CTCI problem 17.1: add two numbers without using + or any arithmetic operators using bitwise XOR for sum and bitwise AND for carry.
• Complexity: Optimal Time and Memory bounds.

This article provides a clear breakdown of CTCI problem 17.1.

1. Context and Problem Statement

CTCI problem 17.1: add two numbers without using + or any arithmetic operators using bitwise XOR for sum and bitwise AND for carry.

2. Technical Code & Mechanics

public static int add(int a, int b) {
    while (b != 0) {
        int sum = a ^ b; // Sum without carry
        int carry = (a & b) << 1; // Carry shifted left
        a = sum;
        b = carry;
    }
    return a;
}

3. Key Takeaways and Edge Cases

Always test boundary conditions and invalid input states.