Decimal to Binary Converter
Convert decimal numbers to binary, including fractions and negative numbers, with the working shown.
Change the values and press Calculate to work out your own figures.
Enter a decimal number to write it in binary.
Show the working
- 170 ÷ 2 = 85 remainder 0
- 85 ÷ 2 = 42 remainder 1
- 42 ÷ 2 = 21 remainder 0
- 21 ÷ 2 = 10 remainder 1
- 10 ÷ 2 = 5 remainder 0
- 5 ÷ 2 = 2 remainder 1
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
- Read the remainders from the bottom up for the whole part
- 170₁₀ = 10101010₂
How to use it
Enter a decimal number to write it in binary.
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
decimal → binary: 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 170 in binary?
10101010.
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
decimal → binary: 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.