Add Two Binary Strings

/*
 * Problem : Process two words.
 * Input   : Two words separated by a space.
 * Output  : The binary sum.
 * Approach: Two binary words.
 * Time    : O(n)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static String solve(String a, String b) {
        // Step 1: Start at the last digit of both words. The carry is what we move to the next digit.
        StringBuilder result = new StringBuilder();
        int i = a.length() - 1;
        int j = b.length() - 1;
        int carry = 0;
        while (i >= 0 || j >= 0 || carry > 0) {
            // Step 2: Add the two digits (a missing digit counts as 0) and the carry.
            int sum = carry;
            if (i >= 0) {
                sum += a.charAt(i--) - '0';
            }
            if (j >= 0) {
                sum += b.charAt(j--) - '0';
            }
            // Step 3: The new digit is sum % 2. The new carry is sum / 2.
            result.append(sum % 2);
            carry = sum / 2;
        }
        // Step 4: We built the answer from the right, so reverse it. Remove leading zeros, but keep one digit.
        String text = result.reverse().toString().replaceFirst("^0+(?=.)", "");
        return text.isEmpty() ? "0" : text;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String a = scanner.next();
        String b = scanner.next();
        System.out.println(solve(a, b));
    }
}