Binary to Decimal Converter
Convert binary numbers to decimal, including fractions and negative numbers, with the working shown.
Change the values and press Calculate to work out your own figures.
Enter a binary number to write it in decimal.
Show the working
- 10101010₂ = 1 × 2⁷ + 0 × 2⁶ + 1 × 2⁵ + 0 × 2⁴ + 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ = 170
How to use it
Enter a binary number to write it in decimal.
Letters stand for digits above 9 (A = 10 … Z = 35) and can be typed in either case; prefixes such as 0b and 0x, spaces and underscores are ignored. Show the working gives each step.
Key facts
binary → decimal: place values Σ dᵢ × bⁱ; repeated division by the new base
How the conversion works
To decimal, multiply each digit by its place value (a power of the base) and add; from decimal, divide by the base repeatedly and read the remainders from the bottom up (for a fraction, multiply by the base and read off the whole parts).
Questions
What is 10101010 in decimal?
170.
Can I convert fractions?
Yes. Digits after the point are converted exactly; if they repeat forever in the new base, the repeating block is shown in parentheses.
Formulas
binary → decimal: place values Σ dᵢ × bⁱ; repeated division by the new base
Sources
Limitations
- Numbers have at most 1,000 characters; Roman numerals cover whole numbers from 1 to 3,999,999.