Sum of Two Integers (Without + or -) Explained

Problem Statement

Given two integers a and b, compute their sum without using the addition (+) or subtraction (-) operators. This problem tests your understanding of bitwise operations, specifically XOR and AND, to simulate binary addition by handling bit sums and carries iteratively.

Example

Input: a = 2, b = 3

Output: 5

Explanation: The sum 2 + 3 is computed as 5 using bitwise operations.

Code

public class Solution {
    public int getSum(int a, int b) {
        while (b != 0) {
            int carry = (a & b) << 1;
            a = a ^ b;
            b = carry;
        }
        return a;
    }

    public static void main(String[] args) {
        Solution sol = new Solution();
        System.out.println(sol.getSum(2, 3)); // 5
    }
}
            

def get_sum(a, b):
    mask = 0xffffffff
    while (b & mask) > 0:
        carry = ((a & b) << 1) & mask
        a = (a ^ b) & mask
        b = carry
    if (a >> 31) & 1:
        return ~(a ^ mask)
    return a

# Example usage
print(get_sum(2, 3))  # 5
            

function getSum(a, b) {
    while (b !== 0) {
        let carry = (a & b) << 1;
        a = a ^ b;
        b = carry;
    }
    return a;
}

// Example usage
console.log(getSum(2, 3)); // 5
            

Explanation

• Use XOR (a ^ b) to compute the sum of bits without considering carries.
• Use AND and left-shift ((a & b) << 1) to compute the carry bits.
• Update a to the sum without carry and b to the carry.
• Repeat until there are no more carries (b == 0).
• Return a as the final sum.

Note