Number systems
Binary
Base 2 uses only the digits 0 and 1. Every value in a computer is ultimately stored as binary; each binary digit is a bit.
Octal
Base 8 uses digits 0–7. Each octal digit represents exactly three bits, which is why octal appears in Unix file permissions (e.g. 755).
Decimal
Base 10 is the everyday number system with digits 0–9; each position is worth ten times the one to its right.
Hexadecimal
Base 16 uses 0–9 and A–F (A = 10 … F = 15). One hex digit is exactly four bits, so two hex digits describe a byte — used for colours (#FF8800), memory addresses and checksums.
Base-36
Base 36 uses 0–9 and A–Z, the most compact case-insensitive alphanumeric system; it is used for short IDs and URL shorteners.
Roman numerals
Roman numerals combine I (1), V (5), X (10), L (50), C (100), D (500) and M (1000). A smaller symbol before a larger one is subtracted (IV = 4, CM = 900). Standard numerals cover 1–3,999.
Decimal to binary table
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
| 31 | 11111 |
| 32 | 100000 |
| 63 | 111111 |
| 64 | 1000000 |
| 100 | 1100100 |
| 127 | 1111111 |
| 128 | 10000000 |
| 255 | 11111111 |
| 256 | 100000000 |
| 1000 | 1111101000 |
| 1024 | 10000000000 |
| 4096 | 1000000000000 |
| 65535 | 1111111111111111 |
Frequently asked questions
What number bases are supported?
Any whole-number base from 2 to 36, plus Roman numerals (1–3,999). Binary, octal, decimal and hexadecimal have shortcuts.
How large can the numbers be?
There is no fixed limit: the converter uses exact big-integer arithmetic, so long binary or hex strings are converted without rounding.
Does it handle negative numbers and prefixes?
Yes. A leading minus sign is kept, and the prefixes 0x, 0b and 0o are accepted for hex, binary and octal input.