Decimal to Binary Converter

Convert decimal numbers to binary format with real-time conversion, input validation, and detailed step-by-step explanations using the division by 2 method.

Range: 0 to 4,294,967,295
Enter a positive integer
Display Options

Example Conversions

Click any example to try it instantly

Simple Example
10
→ 1010
8-bit Max
255
→ 11111111
Power of 2
1024
→ 10000000000
16-bit Max
65535
→ 1111111111111111
Random Number
42
→ 101010
32-bit Max
4294967295
→ 11111111111111111111111111111111

About Decimal to Binary Conversion

Decimal to binary conversion is the process of converting numbers from base-10 (decimal) to base-2 (binary) number system. This conversion is fundamental in computer science and digital electronics.

Key Features:

  • Manual Conversion: Click convert button to see results
  • Optional Real-time Mode: Enable instant conversion as you type
  • Input Validation: Accepts decimal numbers from 0 to 4,294,967,295
  • 32-bit Support: Handle the full range of 32-bit unsigned integers
  • Step-by-step Explanation: Learn the division by 2 method
  • Multiple Formats: View results in different binary formats
  • Copy Functionality: Easily copy results to clipboard
  • Mobile-Friendly: Responsive design that works on all devices

How to Use the Decimal to Binary Converter

  1. Enter your decimal number in the input field (0 to 4,294,967,295)
  2. Choose your preferred display options (steps, formats, grouping)
  3. Click "Convert to Binary" to see the result
  4. Optionally enable "Real-time conversion" for instant results as you type
  5. View the step-by-step conversion process using division by 2
  6. Copy the result using the copy button
  7. Try the example conversions for common decimal values

Decimal to Binary Conversion Process (Division by 2 Method)

The conversion process follows these steps:

  1. Divide by 2: Divide the decimal number by 2
  2. Record Remainder: Note the remainder (0 or 1)
  3. Repeat: Use the quotient for the next division
  4. Continue: Repeat until the quotient becomes 0
  5. Read Backwards: The binary result is the remainders read from bottom to top

Common Decimal Values

10₁₀ = 1010₂
255₁₀ = 11111111₂
1024₁₀ = 10000000000₂
65535₁₀ = 1111111111111111₂

Understanding Binary Representation

Binary numbers use only two digits (0 and 1) and represent values using powers of 2. Each position in a binary number represents a power of 2, starting from 2⁰ on the right.

Applications

  • Computer Programming: Understanding data representation
  • Digital Electronics: Circuit design and logic gates
  • Network Administration: IP address calculations and subnetting
  • Embedded Systems: Microcontroller programming
  • Computer Science Education: Learning number systems