Decimal to Binary

Java coding interview problem for Basic Number Programs: Decimal to Binary.

Converting a Decimal Number to its Binary Representation is one of the most common Java coding interview questions. It helps interviewers evaluate your understanding of number systems, loops, arithmetic operations, and problem-solving skills.

Binary conversion is an important concept in computer science because computers internally store and process data in binary format.

What is a Decimal Number?

A Decimal Number uses the Base-10 number system.

It contains digits from

0 to 9

Examples

What is a Binary Number?

A Binary Number uses the Base-2 number system.

It contains only

0

1

Examples

1010

11001

11111111

10000000000

Every decimal number can be represented in binary.

Decimal to Binary Conversion Table

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
15	1111
16	10000

Real Interview Question

Write a Java program to convert a decimal number into its binary representation without using any built-in methods.

Understanding the Logic

The idea is simple.

Repeatedly divide the decimal number by 2.

At every step,

store the remainder.

Continue until the number becomes zero.

Finally,

read all remainders in reverse order.

Visual Representation

Input

Division Process

13 ÷ 2 = 6

Remainder = 1

↓

6 ÷ 2 = 3

Remainder = 0

↓

3 ÷ 2 = 1

Remainder = 1

↓

1 ÷ 2 = 0

Remainder = 1

Collected Remainders

Read from bottom to top

Therefore

13(decimal)

=

1101(binary)

Why Read in Reverse?

The first remainder becomes the least significant bit (LSB).

The last remainder becomes the most significant bit (MSB).

Example

Collected

Reverse Order

Brute Force Approach

The simplest solution is

Divide the number by 2
Store the remainder
Continue until the number becomes 0
Print the remainders in reverse order

Algorithm

Step 1

Read the decimal number.

Step 2

Handle the special case.

If number == 0

Output = 0

Step 3

Initialize an empty binary number.

Step 4

Repeat while

number > 0

Step 5

Find the remainder.

remainder = number % 2;

Step 6

Store the remainder.

Step 7

Divide the number.

number = number / 2;

Step 8

Repeat until the number becomes zero.

Step 9

Reverse the stored digits.

Step 10

Print the binary number.

Dry Run

Input

Iteration	Number	Remainder	Stored
1	10	0	0
2	5	1	01
3	2	0	010
4	1	1	0101

Reverse

Output

Another Dry Run

Input

Iteration	Number	Remainder	Stored
1	25	1	1
2	12	0	10
3	6	0	100
4	3	1	1001
5	1	1	10011

Reverse

Output

Approach 1 — Using Repeated Division

This is the most common interview solution.

Complete Java Program

public class DecimalToBinary {

    public static void main(String[] args) {

        int number = 25;

        int[] binary = new int[32];

        int index = 0;

        if (number == 0) {

            System.out.println("Binary = 0");

            return;

        }

        while (number > 0) {

            binary[index] = number % 2;

            index++;

            number = number / 2;

        }

        System.out.print("Binary = ");

        for (int i = index - 1; i >= 0; i--) {

            System.out.print(binary[i]);

        }

    }

}

Output

Binary = 11001

Step-by-Step Code Explanation

Step 1

Declare the decimal number.

int number = 25;

Current value

Step 2

Create an array.

int[] binary = new int[32];

The array stores the binary digits (remainders).

Step 3

Initialize the index.

int index = 0;

Initially

index = 0

Step 4

Handle zero.

if (number == 0)

Output

Binary = 0

Step 5

Find the remainder.

number % 2

Example

25 % 2 = 1

Store

Step 6

Divide by 2.

number = number / 2;

Example

Step 7

Repeat

Continue until

number == 0

Each iteration produces one binary digit.

Step 8

Print in reverse.

for (int i = index - 1; i >= 0; i--)

The digits are printed from the last stored remainder to the first.

Example

Stored

Printed

Why Does This Work?

Each division by 2 extracts one binary digit.

The remainder can only be

0

or

1

These remainders represent the binary digits from least significant bit (LSB) to most significant bit (MSB).

Printing them in reverse order produces the correct binary representation.

Advantages of This Approach

Easy to understand.
Uses only arithmetic operators.
Does not rely on built-in Java methods.
Demonstrates understanding of number systems.
Frequently asked in Java coding interviews.
Efficient for integer conversion.

Drawbacks

Although this solution is the most common interview approach, interviewers often ask follow-up questions such as:

Can you solve it using a Stack?
Can you use Integer.toBinaryString()?
Can you create a reusable method?
How would you convert negative numbers?
Which approach is the most efficient?

In the next part, we'll cover:

Stack-based solution
Built-in Java method (Integer.toBinaryString())
Reusable method approach
Time and space complexity
Comparison of all approaches
Common interview mistakes
Frequently asked interview questions
Related coding problems
Key takeaways
Interview tips

Approach 2 — Using Stack

A Stack follows the Last In, First Out (LIFO) principle.

Since binary remainders are generated from Least Significant Bit (LSB) to Most Significant Bit (MSB), a Stack automatically prints them in the correct order.

Logic

Input

Generated Remainders

Push into Stack

Pop Elements

Java Program

import java.util.Stack;

public class DecimalToBinaryStack {

    public static void main(String[] args) {

        int number = 25;

        Stack<Integer> stack = new Stack<>();

        if (number == 0) {

            System.out.println("Binary = 0");

            return;

        }

        while (number > 0) {

            stack.push(number % 2);

            number = number / 2;

        }

        System.out.print("Binary = ");

        while (!stack.isEmpty()) {

            System.out.print(stack.pop());

        }

    }

}

Output

Binary = 11001

Approach 3 — Using Integer.toBinaryString()

Java provides a built-in method for converting decimal numbers to binary.

This is the easiest approach but is usually not preferred in coding interviews because interviewers often want to evaluate your understanding of the conversion algorithm.

Java Program

public class DecimalToBinaryBuiltIn {

    public static void main(String[] args) {

        int number = 25;

        String binary = Integer.toBinaryString(number);

        System.out.println("Binary = " + binary);

    }

}

Output

Binary = 11001

Approach 4 — Using a Reusable Method

Creating a reusable method improves

Code reusability
Readability
Maintainability
Unit testing

Java Program

public class DecimalToBinaryMethod {

    static String convertToBinary(int number) {

        if (number == 0) {

            return "0";

        }

        StringBuilder binary = new StringBuilder();

        while (number > 0) {

            binary.append(number % 2);

            number = number / 2;

        }

        return binary.reverse().toString();

    }

    public static void main(String[] args) {

        int number = 45;

        System.out.println("Binary = " + convertToBinary(number));

    }

}

Output

Binary = 101101

Time Complexity

Array-Based Solution

Operation	Complexity
Time	O(log₂ n)
Space	O(log₂ n)

Stack Solution

Operation	Complexity
Time	O(log₂ n)
Space	O(log₂ n)

Built-in Method

Operation	Complexity
Time	O(log₂ n)
Space	O(log₂ n)

Comparison of All Approaches

Approach	Time	Space	Recommended
Repeated Division + Array	O(log n)	O(log n)	✅ Best for Interviews
Stack	O(log n)	O(log n)	Easy to Understand
Reusable Method	O(log n)	O(log n)	Production Ready
Integer.toBinaryString()	O(log n)	O(log n)	Quick but Less Preferred

Common Mistakes

Mistake 1

Printing the remainders immediately.

Wrong

while (number > 0) {

    System.out.print(number % 2);

    number = number / 2;

}

Output for

becomes

Correct Output

Always print the remainders in reverse order.

Mistake 2

Ignoring the special case

Expected Output

Always check

if (number == 0)

before starting the loop.

Mistake 3

Using floating-point division.

Wrong

number = number / 2.0;

Correct

number = number / 2;

Use integer division.

Mistake 4

Using a fixed-size array without tracking the index.

Always maintain an index to know how many binary digits have been stored.

Mistake 5

Using the built-in method when the interviewer asks

"Convert the number without using built-in methods."

In that case,

implement the repeated division algorithm manually.

Interview Follow-up Questions

Q1. Convert Binary to Decimal.

Q2. Convert Decimal to Octal.

Q3. Convert Decimal to Hexadecimal.

Q4. Convert Binary to Octal.

Q5. Convert Binary to Hexadecimal.

Q6. Count the number of 1s in the binary representation.

Q7. Determine whether a number is a power of 2.

Q8. Explain why the binary digits are printed in reverse order.

Q9. Convert a negative decimal number to binary.

Q10. Compare manual conversion with `Integer.toBinaryString()`.

Key Takeaways

Binary uses only 0 and 1.
Decimal-to-binary conversion is performed by repeatedly dividing the number by 2.
Each remainder represents one binary digit.
The remainders are generated from Least Significant Bit (LSB) to Most Significant Bit (MSB), so they must be printed in reverse order.
The repeated division algorithm is the most common interview solution.
Integer.toBinaryString() is convenient but is usually not accepted when interviewers expect the manual conversion algorithm.
All approaches run in O(log n) time because the number is divided by 2 in every iteration.

Interview Tip

If an interviewer asks:

"Write a Java program to convert a decimal number to binary."

Start with the repeated division by 2 approach. Explain that each division produces one binary digit as a remainder and that these digits are generated from LSB to MSB, requiring them to be printed in reverse order. After implementing the manual solution, mention alternative approaches such as using a Stack, a StringBuilder, or Java's Integer.toBinaryString() method, along with their trade-offs. This demonstrates both algorithmic understanding and knowledge of Java's standard library.

Decimal to Binary

What is a Decimal Number?

What is a Binary Number?

Decimal to Binary Conversion Table

Real Interview Question

Understanding the Logic

Visual Representation

Why Read in Reverse?

Brute Force Approach

Algorithm

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

Step 10

Dry Run

Another Dry Run

Approach 1 — Using Repeated Division

Complete Java Program

Output

Step-by-Step Code Explanation

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Why Does This Work?

Advantages of This Approach

Drawbacks

Approach 2 — Using Stack

Logic

Java Program

Output

Approach 3 — Using Integer.toBinaryString()

Java Program

Output

Approach 4 — Using a Reusable Method

Java Program

Output

Time Complexity

Array-Based Solution

Stack Solution

Built-in Method

Comparison of All Approaches

Common Mistakes

Mistake 1

Mistake 2

Mistake 3

Mistake 4

Mistake 5

Interview Follow-up Questions

Q1. Convert Binary to Decimal.

Q2. Convert Decimal to Octal.

Q3. Convert Decimal to Hexadecimal.

Q4. Convert Binary to Octal.

Q5. Convert Binary to Hexadecimal.

Q6. Count the number of 1s in the binary representation.

Q7. Determine whether a number is a power of 2.

Q8. Explain why the binary digits are printed in reverse order.

Q9. Convert a negative decimal number to binary.

Q10. Compare manual conversion with Integer.toBinaryString().

Related Coding Problems

Key Takeaways

Interview Tip

Q10. Compare manual conversion with `Integer.toBinaryString()`.