What this conversion means in practice
Binary is the native language of digital hardware: each bit is a 0 or 1. Decimal is how humans usually count. Converting between them is the first step in reading register dumps, packet bits, or LED patterns as ordinary numbers.
This page uses the same arbitrary-precision path as the main converter: interpret your string in the source radix, get one exact integer, then print it in the target radix—no floating-point rounding.
Pad binary groups to multiples of four when mentally mapping to hex on other tasks; here you can paste any length and get the exact decimal value.
Mnemonic: Quick sanity: 1010₂ = 10₁₀, 11111111₂ = 255₁₀.
How to convert binary to decimal
Treat your input strictly as a base-2 integer: only digits valid for that base are allowed. The tool converts to an exact integer, then prints it in base 10.
Live example: …2 → …10
Unlike unit conversions with a single scale factor, radix conversion rebuilds the digit sequence. The “expand to decimal, then divide out the target base” algorithm matches what you learn in CS—automated here for any size.
Binary
Definition: Base 2: positional notation using only the digits 0 and 1. Each place is a power of 2.
History and origin: Used formally since Leibniz; became central with Boolean logic and electronic switching.
Current use: Machine code, buses, flags, and any representation of bits in computing.
Decimal
Definition: Base 10: the everyday positional system using digits 0–9.
History and origin: Linked to counting on ten fingers; dominant globally for human-facing arithmetic.
Current use: General arithmetic, finance, and human-readable magnitudes before re-encoding to other bases.
Binary to Decimal conversion table
| Binary (base 2) | Decimal (base 10) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 1010 | 10 |
| 11111111 | 255 |
| 100000000 | 256 |
Binary to Decimal FAQ
How do I convert binary to decimal by hand?
Sum each bit times 2 raised to its place index (starting at 0 on the right). Or use this tool for long strings.
Do I include a 0b prefix?
No. Enter only digits 0 and 1. Strip language prefixes like 0b before pasting.
Why is my binary invalid?
Binary only allows 0 and 1. Any other character triggers the validation hint below the input.