Free Decimal to Binary Converter Online
Convert decimal numbers to binary, octal, and hexadecimal with step-by-step conversion explanations.
Features
- Multi-base output - Binary, octal, and hexadecimal
- Batch conversion - Convert multiple numbers at once
- Step-by-step - See the conversion process
- Quick presets - Common values for fast input
- Bit count - See how many bits are needed
How Decimal to Binary Works
Binary uses only 0s and 1s. To convert decimal to binary, repeatedly divide by 2 and record remainders:
Example: 42 to Binary
| Divide | Quotient | Remainder |
|---|---|---|
| 42 ÷ 2 | 21 | 0 |
| 21 ÷ 2 | 10 | 1 |
| 10 ÷ 2 | 5 | 0 |
| 5 ÷ 2 | 2 | 1 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
Read remainders bottom to top: 101010
Common Decimal to Binary Conversions
| Decimal | Binary | Bits |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 1 | 1 |
| 8 | 1000 | 4 |
| 16 | 10000 | 5 |
| 255 | 11111111 | 8 |
| 256 | 100000000 | 9 |
| 1024 | 10000000000 | 11 |
Number Base Reference
| Base | Name | Digits |
|---|---|---|
| 2 | Binary | 0, 1 |
| 8 | Octal | 0-7 |
| 10 | Decimal | 0-9 |
| 16 | Hexadecimal | 0-9, A-F |
Use Cases
Programming
- Understanding computer memory
- Bitwise operations
- Data representation
Computer Science
- Data structures
- Algorithm analysis
- Network protocols
Education
- Learning number systems
- Math exercises
- Digital logic
FAQs About Decimal to Binary
What's the largest number supported?
JavaScript handles numbers up to about 9 quadrillion accurately.
Can I convert negative numbers?
Yes! We show the binary with a negative sign prefix.
How is this used in computing?
All computer data is ultimately stored as binary - 0s and 1s.
What's the relationship to bytes?
8 bits = 1 byte. A byte can represent 0-255 in decimal.
Why Use Our Decimal to Binary Converter?
- Free to use - No registration
- Multiple bases - Binary, octal, hex
- Step-by-step - Learn the conversion
- Batch mode - Convert many numbers
- Reference table - Common values