Binary Converter
Type in any field — all four number systems update instantly.
Quick Reference Table
| Decimal | Binary | Hex | Octal |
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Number Systems Explained
The standard system humans use, with digits 0–9. Each position is a power of 10. "255" means 2×100 + 5×10 + 5×1.
Used internally by computers. Only digits 0 and 1. Each position is a power of 2. "11111111" = 128+64+32+16+8+4+2+1 = 255.
Uses digits 0–9 and letters A–F (where A=10, B=11 … F=15). One hex digit represents exactly 4 binary bits. "FF" = 15×16 + 15 = 255.
Uses digits 0–7. Each octal digit represents 3 binary bits. "377" = 3×64 + 7×8 + 7 = 255. Used in Unix permissions.
Frequently Asked Questions
This converter uses JavaScript's built-in integer parsing, which safely handles integers up to 2^53−1 (9,007,199,254,740,991) in decimal. For cryptographic or hardware purposes requiring exact 64-bit arithmetic, use a dedicated tool with BigInt support.
Electronic circuits have two stable states: on (high voltage = 1) and off (low voltage = 0). Binary maps perfectly to this physical reality. It is far simpler to build reliable hardware with two states than ten.
Computers represent negative numbers using Two's Complement: invert all bits of the positive representation and add 1. For example, −1 in 8-bit is 11111111. This converter shows the unsigned binary representation; for two's complement use a dedicated signed integer tool.