Decimal to Binary Converter
Convert decimal numbers to binary code instantly with our free online tool. Supports both whole numbers and fractional decimals with detailed conversion steps and examples.
Decimal to Binary Converter
Enter a decimal number to convert it to binary code
Instant Conversion
Get binary results in milliseconds
Accurate Results
Precision conversion with detailed steps
Mobile Friendly
Works perfectly on all devices
Decimal to Binary Conversion Examples
Example 1: Whole Number Conversion
Convert 428 to binary:
Reading remainders from bottom to top: 110101100
Example 2: Fractional Number Conversion
Convert 0.4 to binary:
Result: .011001 (repeating pattern)
Decimal to Binary Conversion Table
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0000 | 8 | 1000 |
| 1 | 0001 | 9 | 1001 |
| 2 | 0010 | 10 | 1010 |
| 3 | 0011 | 11 | 1011 |
| 4 | 0100 | 12 | 1100 |
| 5 | 0101 | 13 | 1101 |
| 6 | 0110 | 14 | 1110 |
| 7 | 0111 | 15 | 1111 |
| 16 | 10000 | 120 | 1111000 |
| 17 | 10001 | 240 | 11110000 |
| 18 | 10010 | 350 | 101011110 |
| 19 | 10011 | 500 | 111110100 |
| 20 | 10100 | 1000 | 1111101000 |
Frequently Asked Questions
How do I convert decimal to binary manually?
To convert decimal to binary manually:
- For whole numbers: Repeatedly divide by 2 and record remainders. Read remainders from bottom to top.
- For fractions: Multiply by 2 repeatedly and record integer parts. Read integers from top to bottom.
Can this converter handle decimal numbers with fractions?
Yes! Our converter supports both whole numbers and fractional decimal numbers. For example, 428.4 will be converted to 110101100.011001.
What is the maximum decimal number I can convert?
The converter can handle very large decimal numbers. However, for practical purposes, we recommend numbers up to 10 digits for optimal performance and readability.
Why do some decimal fractions result in repeating binary patterns?
Some decimal fractions cannot be represented exactly in binary and result in repeating patterns. For example, 0.1 in decimal becomes 0.0001100110011... in binary, repeating infinitely.
Is this converter free to use?
Yes! Our Decimal to Binary Converter is completely free to use with no registration required. Convert as many decimal numbers to binary as you need.
Understanding Decimal to Binary Conversion
What is Decimal to Binary Conversion?
Decimal to binary conversion is the process of transforming numbers from our familiar base-10 (decimal) system to the base-2 (binary) system used by computers. In the decimal system, we use digits 0-9, while the binary system uses only 0 and 1.
Why is Decimal to Binary Conversion Important?
Understanding decimal to binary conversion is crucial for:
- Computer Programming: Binary is the fundamental language of computers
- Digital Electronics: Understanding how digital circuits process information
- Network Protocols: IP addresses and subnet masks often require binary understanding
- Data Storage: Understanding how information is stored in memory
- Cryptography: Many encryption algorithms work with binary data
How Our Decimal to Binary Converter Works
Our converter uses sophisticated algorithms to handle both whole numbers and decimal fractions. For whole numbers, it repeatedly divides by 2 and records remainders. For fractions, it multiplies by 2 and records integer parts. This ensures accurate conversion for any decimal input.
Common Uses for Decimal to Binary Conversion
- Converting IP addresses for network configuration
- Understanding binary representation in programming
- Educational purposes in computer science courses
- Digital signal processing applications
- Error detection and correction in data transmission
Tips for Manual Decimal to Binary Conversion
- Practice with small numbers: Start with numbers 0-15 to understand the pattern
- Use the division method: For whole numbers, divide by 2 and record remainders
- Use the multiplication method: For fractions, multiply by 2 and record integer parts
- Check your work: Convert back from binary to verify your result
- Learn common patterns: Memorize binary for 0-15 for quick reference