Number base converters translate between decimal (base 10), binary (base 2), hex (base 16), and octal (base 8). Essential for programmers, network engineers, students, and anyone debugging at byte level.
This guide covers conversion methods and worked examples.
Convert Number Bases — Free
Decimal, binary, hex, octal — all directions instantly.
Number Bases Explained
| Base | Digits Used | Use |
|---|---|---|
| Decimal (10) | 0-9 | Everyday math |
| Binary (2) | 0, 1 | Computer logic |
| Octal (8) | 0-7 | Unix file permissions |
| Hex (16) | 0-9, A-F | Memory addresses, colors |
Conversion Examples
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 10 | 1010 | 12 | A |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
| 1024 | 10000000000 | 2000 | 400 |
Conversion Methods
Decimal to Binary
Divide by 2, write remainders bottom-up:
13 ÷ 2 = 6 r 1
6 ÷ 2 = 3 r 0
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1
Result: 1101Binary to Decimal
Multiply each digit by 2^position (right to left):
1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13Decimal to Hex
Same as binary but divide by 16. Use A-F for 10-15.
Real Use Cases
- Color codes — #FF5733 (hex)
- File permissions — 755, 644 (octal)
- Memory addresses — 0x7FFE (hex)
- Bitwise operations — programming
- Network masks — IP subnets
- ASCII codes — character to number
How to Use the Tool (Step by Step)
- 1
Enter Number
In any base.
- 2
Pick Source Base
Decimal, binary, hex, octal.
- 3
See All Conversions
Tool shows all 4 representations.
- 4
Verify with Manual
For learning.
- 5
Copy Result
Use in code or documents.
Frequently Asked Questions
Why is hex used in computing?+−
Each hex digit = 4 binary bits, making memory and color values shorter and human-readable.
Why do file permissions use octal?+−
3 permission bits (read, write, execute) per group fits perfectly in 1 octal digit (0-7).
Can negative numbers convert to binary?+−
Yes — using two's complement representation. Most converters handle this for signed integers.
Why isn't there base 11?+−
No conventional use. Base 10 (decimal) and powers of 2 (binary, octal=2³, hex=2⁴) are practical.
How big can binary numbers get?+−
Unlimited mathematically. Computers limit to 32-bit, 64-bit, etc., based on hardware.
What is 0xFF in decimal?+−
255. FF in hex = 16×15 + 15 = 255.
Convert Number Bases — Free
Decimal, binary, hex, octal — all directions instantly.
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