Number Base Converter
Convert numbers between binary, decimal, octal, and hexadecimal instantly.
How to Use the Number Base Converter
Different number systems use a different count of digits, but they all describe the same underlying quantity. To convert:
- Enter your value in the input field.
- Choose its base — decimal, binary, octal, or hexadecimal.
- Read the equivalents in all four bases, calculated instantly and exactly.
The Four Common Number Systems
- Decimal (base 10): The everyday system, using digits 0–9.
- Binary (base 2): Uses only 0 and 1 — the native language of computers, where each digit is a "bit".
- Octal (base 8): Uses digits 0–7. Historically common in computing and still used for things like Unix file permissions.
- Hexadecimal (base 16): Uses 0–9 then A–F. A compact stand-in for binary, used for memory addresses and colour codes.
Worked Example
Example: The Decimal Number 255
Decimal: 255
Hexadecimal: FF (15 × 16 + 15)
Octal: 377 (3 × 64 + 7 × 8 + 7)
Binary: 11111111 (eight 1-bits — the largest value one byte can hold)
Quick Reference: 0 to 16 in Every Base
This table shows how the same values look across all four systems:
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 4 | 100 | 4 | 4 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
Where Number Bases Are Used
- Web colours: Hex codes like
#FF5733encode red, green, and blue as three pairs of hex digits. - Memory & addresses: Programmers read memory addresses in hexadecimal because it maps cleanly to binary.
- File permissions: Unix/Linux permissions (like
chmod 755) are written in octal. - Networking: Subnet masks and MAC addresses rely on binary and hexadecimal.
Frequently Asked Questions
A number base (or radix) is how many unique digits a system uses. Decimal is base-10 (digits 0–9), binary is base-2 (0–1), octal is base-8 (0–7), and hexadecimal is base-16 (0–9 then A–F). The same quantity can be written in any base.
Repeatedly divide the decimal number by 2 and record the remainders, then read them bottom to top. For example, 13 in binary is 1101. This converter does it instantly for you in either direction.
Hexadecimal is a compact way to represent binary: each hex digit maps exactly to 4 binary bits. It is widely used for memory addresses, colour codes (like #FF5733), and byte values because it is far shorter and easier to read than long binary strings.
In hexadecimal, A=10, B=11, C=12, D=13, E=14, and F=15. They extend the digit set beyond 9 so that base-16 has 16 unique symbols.
Yes. It uses arbitrary-precision (BigInt) arithmetic, so conversions stay exact even for numbers far larger than a standard calculator can handle without rounding.
Note: This converter handles non-negative integers using arbitrary-precision arithmetic, so results are exact even for very large numbers. Fractional (decimal-point) and negative-base conversions are not supported.