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Convert Decimal to Binary in Java

beginner· Numbers · Number Conversion

Problem

Binary is base 2: every digit is a bit worth a power of two, so 45 is written 101101 because 32 + 8 + 4 + 1 = 45.

Given a non-negative integer, print its binary representation.

Input

45

Output

101101

Java Program

Java

public class DecimalToBinary {
    public static void main(String[] args) {
        int number = 45;

        if (number == 0) {
            System.out.println("Binary of 0: 0");
            return;
        }

        StringBuilder binary = new StringBuilder();
        int n = number;
        while (n > 0) {
            binary.append(n % 2); // remainder is the next bit, lowest bit first
            n /= 2;
        }

        System.out.println("Binary of " + number + ": " + binary.reverse()); // bits were collected backwards
    }
}

▶ Run Code

Output

Binary of 45: 101101

Core Logic

Dividing by 2 strips off the lowest bit each time, and the remainder of that division is exactly the bit that was removed.

How It Works

1n % 2 gives the current lowest bit, 0 or 1, which is appended to binary.
2n /= 2 drops that bit, shifting the remaining bits down by one place.
3The loop repeats until n reaches 0, so every bit is collected.
4The bits come out lowest first, so binary.reverse() puts them in reading order; 0 is handled separately because the loop would never run for it.

45 → remainder 1, 22 → 0, 11 → 1, 5 → 1, 2 → 0, 1 → 1. Read from last to first, the remainders spell 101101.

💡

Key Point: This loop only handles non-negative values — negative numbers in Java are stored in two's complement, which the built-in method shows as a full 32-bit pattern.

Complexity

Time Complexity: O(log n)Space Complexity: O(log n)

Why: The number halves on every step, so the loop runs once per bit, and the builder stores one character per bit.

Key Concepts

while loopmodulo operatorStringBuilder.reverse()

Approach 2: Using Integer.toBinaryString()

Java

public class DecimalToBinaryBuiltIn {
    public static void main(String[] args) {
        int number = 45;
        System.out.println("Binary of " + number + ": " + Integer.toBinaryString(number));
        System.out.println("Binary of -45: " + Integer.toBinaryString(-45)); // two's complement, all 32 bits
    }
}

▶ Run Code

Output

Binary of 45: 101101
Binary of -45: 11111111111111111111111111010011

Core Logic

The standard library already does this conversion, and it also handles negative numbers by showing their two's complement bit pattern.

How It Works

1Integer.toBinaryString(45) returns the string "101101" directly.
2Leading zeros are left off, just like in the manual version.
3For -45 it returns all 32 bits of the two's complement form, which starts with a run of 1s.

-45 becomes 11111111111111111111111111010011 — the same bits Java uses to store it in memory.

💡

Key Point: Use the built-in in real code; write the loop in interviews, where the point is to show you understand how base conversion works.

Complexity

Time Complexity: O(log n)Space Complexity: O(log n)

Why: The method still produces one character per significant bit (up to 32 for an int).

Key Concepts

Integer.toBinaryString()two's complement

Interview Questions

How do you pad the binary string to 8 bits?

String.format("%8s", Integer.toBinaryString(n)).replace(' ', '0').

How do you convert a negative number to binary?

Integer.toBinaryString(-n) shows its 32-bit two's complement form. Integer.toString(n, 2) keeps a minus sign instead.

← Previous

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