Binary to Decimal Converter
Convert a binary (base 2) number to decimal (base 10) instantly. As an example, 11111111 = 255. It runs entirely in your browser.
| Base | This number |
|---|---|
| Binary (base 2) | — |
| Octal (base 8) | — |
| Decimal (base 10) | — |
| Hexadecimal (base 16) | — |
How to convert binary to decimal
Each digit of a binary number carries a weight that is a power of 2. Multiply every digit by 2 raised to its position (counting from 0 on the right) and add the results to get the decimal value:
1 × 2^7 + 1 × 2^6 + 1 × 2^5 + 1 × 2^4 + 1 × 2^3 + 1 × 2^2 + 1 × 2^1 + 1 × 2^0 = 255
Worked example: 11111111 in decimal
Reading 11111111 as base 2: 1 × 27 (= 128) + 1 × 26 (= 64) + 1 × 25 (= 32) + 1 × 24 (= 16) + 1 × 23 (= 8) + 1 × 22 (= 4) + 1 × 21 (= 2) + 1 × 20 (= 1) = 255 in decimal, which is 255 in decimal.
Binary, octal, decimal & hexadecimal reference table
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 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 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 100 | 1100100 | 144 | 64 |
| 128 | 10000000 | 200 | 80 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
| 1024 | 10000000000 | 2000 | 400 |
About binary and decimal
Binary: Binary is base-2: every digit (bit) is 0 or 1. It is how computers store and process all data at the hardware level.
Decimal: Decimal is base-10, the everyday number system using digits 0–9.
Frequently asked questions
- What is 11111111 binary in decimal?
- 11111111 in binary (base 2) equals 255 in decimal (base 10), which is 255 in decimal.
- How do I convert binary to decimal by hand?
- Multiply each binary digit by 2 raised to its position (starting at 0 on the right) and add the results. For 11111111: 1×2^7 + 1×2^6 + 1×2^5 + 1×2^4 + 1×2^3 + 1×2^2 + 1×2^1 + 1×2^0 = 255.
- Is this exact for very large numbers?
- Yes. The converter uses big-integer (BigInt) arithmetic in your browser, so even very long binary values convert to decimal with no rounding or precision loss.
- Which characters are valid in binary?
- Base-2 binary uses the digits 0 and 1. Spaces, underscores and an optional 0x/0b/0o prefix are ignored; any other character is flagged as invalid.