Convert Binary to Decimal
Convert a binary number to decimal and check the result instantly.
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The binary to decimal converter turns a sequence of ones and zeros into the number it represents in base 10. The result appears as you type, alongside the same value in octal and hexadecimal.
How the calculation works
Each position in a binary number is worth twice the one to its right. Converting means adding up the powers of 2 where there is a one:
| Bit | 1 | 0 | 1 | 1 |
|---|---|---|---|---|
| Position | 2³ | 2² | 2¹ | 2⁰ |
| Value | 8 | 0 | 2 | 1 |
Adding the last row: 8 + 0 + 2 + 1 = 11. The trick for doing it in your head is to sweep left to right, doubling the running total and adding the current bit: 1 → 2+0=2 → 4+1=5 → 10+1=11.
Values worth recognising
| Binary | Decimal | Why it shows up |
|---|---|---|
1111 | 15 | A full nibble, one hexadecimal digit |
1111 1111 | 255 | A full byte, the max of an RGB channel |
1 0000 0000 | 256 | The number of distinct values in a byte |
111 1111 1111 1111 | 32767 | The max of a signed 16-bit integer |
Need the other direction? Go to decimal to binary.
How to use Binary to Decimal
- 1
Type the binary number
Enter the sequence of ones and zeros in the input field. You do not need to separate it or pad it to eight bits.
- 2
Read the decimal instantly
The base 10 result appears highlighted as soon as you type the first digit, with no button to press.
- 3
Check for invalid digits
If a character other than 0 or 1 slips in, it is flagged next to the input with the exact offender.
- 4
Use the other bases too
Below the result you get the same number in octal and hexadecimal, each with its own copy button.
Frequently asked questions
How do you convert binary to decimal by hand?
Multiply each bit by the power of 2 matching its position, starting at 2⁰ on the right, then add the results. So 1011 is 8 + 0 + 2 + 1 = 11.
What is 1111 1111 in decimal?
255. It is the maximum value of an 8-bit byte, which is exactly why RGB color channels run from 0 to 255.
Is there a digit limit?
No. The conversion uses arbitrary-precision arithmetic, so a 64-bit number or larger comes out exact, without the rounding an ordinary calculator would apply.
Can I paste binary with spaces between bytes?
Yes. Spaces, underscores and dots are ignored, so 1111 1111 and 11111111 give the same result: 255. The 0b prefix from programming languages is accepted too.
Does it handle negative numbers?
It accepts a leading minus sign and keeps it: -1011 gives -11. What it does not do is read two's complement, so 11111111 gives 255 and not -1, because that would require knowing the number's bit width.