Step-by-step calculation
Enter binary digits to see the power-of-two expansion.
Base-2 to base-10
Binary to Decimal Converter
Paste a binary number and get the decimal value, hexadecimal value, and a readable powers-of-two breakdown.
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Hex-
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Binary place values
Binary is base-2, so every position is a power of two. Reading from right to left, the places are 1, 2, 4, 8, 16, 32, and so on.
For 1010, the active positions are 8 and 2. Add them together and the decimal result is 10.
| Binary | Decimal | Notes |
|---|---|---|
1 | 1 | Smallest non-zero binary value |
10 | 2 | One power of two |
1010 | 10 | 8 + 2 |
1111 | 15 | 8 + 4 + 2 + 1 |
10000 | 16 | 2 to the fourth power |
11111111 | 255 | Maximum unsigned 8-bit value |
The converter shows the decimal answer first, but the step-by-step expansion is the part that helps when you are checking homework, debugging a flag value, or reading a protocol field. Each binary digit either contributes its power-of-two value or contributes zero. Adding only the active positions gives the final base-10 number.
Spaces are ignored, so grouped byte strings such as 01000001 01000010 can still be evaluated. For very large values, use the result as a quick reference and double-check any environment that has fixed integer limits, because programming languages may store numbers with different precision rules.
Common binary to decimal searches
Frequent examples include 1010 to decimal, 1001 to decimal, 11111111 to decimal, 8-bit binary to decimal, and 16-bit binary to decimal. Signed binary and two's complement use an additional interpretation rule, so an unsigned calculator result should be checked against the signed format required by your class, protocol, or programming language.