Decimal to binary converter
Enter a whole or fractional decimal number to get its binary form in 4-bit groups, with the full working.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter decimal number and fraction digits if it does not end.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Whole part: divide by 2 again and again, note each remainder and read the remainders from last to first. Fraction part: multiply the fraction by 2 again and again and take the whole digit each time.
Example
Inputs: Decimal number = 42, Fraction digits if it does not end = 24. Result: Result in binary: 101010.
42
101010
Limits and caveats
- Negative numbers keep a minus sign in front of the magnitude; they are not shown in two's complement.
- Up to 2000 digits before the point and 200 after it.
- A fraction that does not end in the new base is cut at the number of digits you choose, without rounding.
Questions about this tool
How do I convert 13 to binary by hand?
Divide by 2 and keep the remainders: 13 gives 6 r1, then 3 r0, then 1 r1, then 0 r1. Read them bottom up: 1101.
Why does 0.1 never end in binary?
Its denominator 10 contains the factor 5, and binary can only write fractions whose denominator is a power of 2 exactly, so the pattern 0011 repeats forever.
Can I convert a negative number?
Yes, the result keeps a minus sign, such as -101. For the fixed-width form computers use, open the two's complement tool.