add-binary-numbers.md

In Java, you can add binary numbers in multiple ways. Here are the best approaches:

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🔹 Method 1: Using Integer.parseInt() (Easy & Built-in)

This method converts binary strings to decimal, adds them, and converts the result back to binary.

public class BinaryAddition {
    public static void main(String[] args) {
        String a = "110"; // Binary of 6
        String b = "101"; // Binary of 5

        String result = addBinary(a, b);
        System.out.println("Sum: " + result); // Output: 1011 (Binary of 11)
    }

    public static String addBinary(String a, String b) {
        int num1 = Integer.parseInt(a, 2); // Convert binary to decimal
        int num2 = Integer.parseInt(b, 2);
        int sum = num1 + num2; // Add decimal numbers

        return Integer.toBinaryString(sum); // Convert back to binary
    }
}

✅ Output:

Sum: 1011

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🔹 Method 2: Manual Binary Addition (Bitwise & Carry)

This method adds binary numbers manually like how we do it on paper.

public class ManualBinaryAddition {
    public static void main(String[] args) {
        String a = "110"; // Binary of 6
        String b = "101"; // Binary of 5

        String result = addBinary(a, b);
        System.out.println("Sum: " + result); // Output: 1011 (Binary of 11)
    }

    public static String addBinary(String a, String b) {
        StringBuilder result = new StringBuilder();
        int i = a.length() - 1, j = b.length() - 1, carry = 0;

        while (i >= 0 || j >= 0 || carry > 0) {
            int sum = carry;
            if (i >= 0) sum += a.charAt(i--) - '0'; // Convert char to int (0 or 1)
            if (j >= 0) sum += b.charAt(j--) - '0';

            result.append(sum % 2); // Append 0 or 1
            carry = sum / 2; // Carry will be 1 if sum is 2 or 3
        }

        return result.reverse().toString();
    }
}

✅ Output:

Sum: 1011

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🔹 Method 3: Using BigInteger for Large Numbers

If you're dealing with very large binary numbers, BigInteger is the best choice.

import java.math.BigInteger;

public class BigIntegerBinaryAddition {
    public static void main(String[] args) {
        String a = "110110101101101011"; // Large binary number
        String b = "101011011010110110";

        String result = addBinary(a, b);
        System.out.println("Sum: " + result);
    }

    public static String addBinary(String a, String b) {
        BigInteger num1 = new BigInteger(a, 2); // Convert binary to BigInteger
        BigInteger num2 = new BigInteger(b, 2);
        BigInteger sum = num1.add(num2); // Perform addition

        return sum.toString(2); // Convert back to binary
    }
}

✅ Handles large binary numbers efficiently.

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🔹 Summary: Which Method to Use?

Method	Best For	Performance
Integer.parseInt()	Small binary numbers	O(1)
Manual Carry-based Addition	Learning how binary addition works	O(n)
BigInteger	Very large binary numbers	O(n)

🚀 Use Integer.parseInt() for simple cases. Use BigInteger for large numbers.