Decimal to Binary

A Decimal to Binary Converter is a tool used to convert numbers from the decimal system (base-10)—which we use in everyday arithmetic—to the binary system (base-2), the foundational language of computers. This conversion is essential in fields like computer science, digital electronics, and programming.

The decimal system uses digits from 0–9, while the binary system uses only 0 and 1.

Conversion Principle:

To convert a decimal number to binary, divide the number by 2 repeatedly and record the remainders. Read the remainders from bottom to top to get the binary result.

Example:

Decimal 13

→ 13 ÷ 2 = 6 remainder 1

→ 6 ÷ 2 = 3 remainder 0

→ 3 ÷ 2 = 1 remainder 1

→ 1 ÷ 2 = 0 remainder 1

→ Binary = 1101

Common Uses for Decimal to Binary Conversion:

• Computer Programming: All data, memory addresses, and logic operations are binary-based.
• Embedded Systems & Microcontrollers: Binary is used for machine-level operations.
• Digital Electronics: Binary logic drives electronic gates and circuits.
• Networking: IP addressing, subnet masks, and protocols involve binary values.
• Mathematical Education: Understanding number systems and base conversions.

Key Features of Decimal to Binary Converter:

• Accurate Conversion: Converts any decimal number (whole or fractional) into binary without error.
• Instant Results: Real-time display as you input values.
• Fractional Support: Supports both integer and decimal point binary conversions (e.g., 10.25 → 1010.01).
• Bit Visualization: Shows binary digits and position for better understanding.
• User-Friendly: Designed for both technical users and beginners.
• Educational Tool: Great for learning how number systems interact.

The Decimal to Binary Converter makes it simple to represent human-friendly numbers in machine-readable format.

Enter the Decimal Number:

Input any base-10 number, such as 25 or 12.5.

View the Binary Result:

The converter instantly provides the binary equivalent.

Understand the Process:

The converter shows step-by-step division or multiplication to clarify the logic.

Use the Output as Needed:

Apply it in programming, education, circuit design, and more.

For Integers:

Example 1: Decimal: 18

→ 18 ÷ 2 = 9 remainder 0

→ 9 ÷ 2 = 4 remainder 1

→ 4 ÷ 2 = 2 remainder 0

→ 2 ÷ 2 = 1 remainder 0

→ 1 ÷ 2 = 0 remainder 1

→ Binary = 10010

For Fractions:



Example 2: Decimal: 10.625

→ Integer part: 10 → 1010

→ Fractional part:

 0.625 × 2 = 1.25 → 1

 0.25 × 2 = 0.5 → 0

 0.5 × 2 = 1.0 → 1

→ Binary = 1010.101

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

20

10100

25

11001

Steps to Convert Decimal to Binary:

For Integers:

1. Divide the decimal number by 2.
2. Write down the remainder (0 or 1).
3. Repeat step 1 with the quotient until you reach 0.
4. Read the remainders in reverse order.

For Fractions:

1. Multiply the decimal part by 2.
2. Record the whole number part of the result.
3. Repeat the multiplication with the new fractional part.
4. Stop after desired precision or when fractional part becomes 0.