Lesson 24. Converting Decimal to Binary in Java | Learn Basic Java

In programming, converting a number from the decimal system (base 10) to the binary system (base 2) is a common problem. Java provides several ways to perform this conversion, including:

• Using repeated division by 2 (manual algorithm).
• Using Java’s built-in method (Integer.toBinaryString()).
• Using recursion.

This article will guide you through each method with detailed explanations and examples.

What are the Decimal and Binary Systems?

• Decimal System (Base 10):

  • The standard number system used in daily life.
  • Consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

• Binary System (Base 2):

  • Uses only 2 digits: 0 and 1.
  • Computers use the binary system to store and process data.

Example:

• 10 (decimal) → 1010 (binary).
• 25 (decimal) → 11001 (binary).

Method 1: Converting Decimal to Binary Using Repeated Division by 2

This method involves repeatedly dividing the decimal number by 2 and recording the remainder, then reading the remainders in reverse order.

Steps to Convert:

1. Divide the decimal number by 2.
2. Record the remainder.
3. Continue dividing the quotient by 2 until it becomes 0.
4. Read the remainders in reverse order to get the binary result.

Example: Convert 10 (decimal) to binary

Result (read in reverse): 1010 (binary)

Java Implementation

import java.util.Scanner;

public class DecimalToBinary {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter a decimal number: ");
        int decimal = scanner.nextInt();
        scanner.close();

        System.out.println("Binary equivalent: " + convertToBinary(decimal));
    }

    public static String convertToBinary(int decimal) {
        StringBuilder binary = new StringBuilder();

        while (decimal > 0) {
            int remainder = decimal % 2;
            binary.insert(0, remainder); // Insert remainder at the beginning
            decimal /= 2;
        }

        return binary.length() > 0 ? binary.toString() : "0"; // Return "0" if input is 0
    }
}

Explanation:

• Uses a while loop to repeatedly divide the number by 2.
• Uses StringBuilder.insert(0, remainder) to build the binary number from left to right.
• Handles the case where input is 0 and returns "0".

Method 2: Using Java’s Built-in Integer.toBinaryString() Method

Java provides the built-in method Integer.toBinaryString(int number), making the conversion very simple.

Java Implementation

import java.util.Scanner;

public class DecimalToBinaryBuiltIn {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter a decimal number: ");
        int decimal = scanner.nextInt();
        scanner.close();

        // Using Java's built-in method
        String binary = Integer.toBinaryString(decimal);
        System.out.println("Binary equivalent: " + binary);
    }
}

Explanation:

• Extremely simple and efficient.
• Uses Java’s built-in library, eliminating the need for a manual algorithm.

Method 3: Using Recursion to Convert Decimal to Binary

Recursion can also be used to convert a decimal number to binary.

Java Implementation

import java.util.Scanner;

public class DecimalToBinaryRecursive {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter a decimal number: ");
        int decimal = scanner.nextInt();
        scanner.close();

        System.out.println("Binary equivalent: " + convertToBinary(decimal));
    }

    public static String convertToBinary(int decimal) {
        if (decimal == 0) {
            return "0";
        } else if (decimal == 1) {
            return "1";
        }
        return convertToBinary(decimal / 2) + (decimal % 2);
    }
}

Explanation:

• Uses recursion until the number is reduced to 0 or 1.
• Builds the binary number by concatenating the remainder to the result.

Comparison of Methods

Conclusion

• Use the while loop method if you want to understand the algorithm.
• Use Integer.toBinaryString() for the simplest and most efficient solution.
• Use recursion if you want to practice recursion techniques.

In real-world applications, Integer.toBinaryString() is the best choice due to its simplicity and performance!

Next article: Lesson 25: do-while Loop in Java