Binary to Decimal Converter
Convert binary numbers to decimal, including fractional binary and the signed two’s-complement interpretation.
Your inputs
Results
Decimal (unsigned)
255
- As a signed 8-bit two’s-complement integer
- -1
- Hexadecimal
- FF
- Bits
- 8
✓Exact calculation — rounded only for display
What this calculator does
Binary is base 2. The same bit pattern can mean different numbers depending on whether it is signed.
Formula and method
Unsigned value = Σ bitₖ × 2^k; signed (two’s complement) = unsigned − 2ⁿ if the top bit is 1
Worked example
Calculated by this tool with its default inputs:
Inputs
- Binary number (spaces and a binary point allowed): 1111 1111
Results
- Decimal (unsigned): 255
- As a signed 8-bit two’s-complement integer: -1
- Hexadecimal: FF
- Bits: 8
How to read the results
11111111 is 255 unsigned but −1 as a signed 8-bit number.
Assumptions and limitations
- Spaces and a 0b prefix are allowed.
Questions
What is two’s complement?
The standard way computers store signed integers.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy