Decimal to Binary
Decimal to binary converts one decimal number, including a fractional part, with calculation steps.
Default: up to 32 binary fractional digits, truncated toward zero if needed. Terminating results stop earlier. Integer digits are not truncated.
Calculation steps
Frequently asked questions
How do I convert decimal to binary?
Enter one decimal number and select Convert to binary. Divide the integer part by two repeatedly, then read the remainders from bottom to top. For a fractional part, multiply it by two repeatedly and read the integer digits from top to bottom. Open Calculation steps to see the operations for your input.
Does this decimal to binary calculator accept fractions?
Yes. Use a point, such as 13.625, rather than a comma. A leading or trailing point is accepted if at least one digit is present. A fractional binary expansion may continue indefinitely; the selected maximum controls how many fractional digits this page displays.
What does a fraction look like in binary?
13.625 produces 1101.101. The integer remainders produce 1101; multiplying the fractional part by two produces 1, 0 and 1, then the remainder reaches zero. In contrast, 0.1 has a repeating binary expansion and is truncated at the chosen limit.
How many fractional places does the converter keep?
The default maximum is 32 binary fractional digits. You can choose 16 or 64 instead. If a nonzero remainder remains at that limit, the result is truncated toward zero without rounding, and the status says so. If the remainder becomes zero earlier, calculation stops at that point. The limit applies to fractional digits only.
Can I enter negative numbers, spaces or scientific notation?
Yes. Use an optional leading plus or minus sign. Whitespace groups one number and is removed, so 1 3.6 2 5 means 13.625, not a batch. Scientific notation such as 1.5e2 is accepted. Commas, binary prefixes, octal prefixes, hexadecimal prefixes and other characters are rejected. Invalid input clears the previous result.
What are the input limits?
This decimal to binary converter accepts one number per run, up to 1,000 decimal digits before the exponent and 10,000 total input characters including whitespace. The exponent must be between -1000 and 1000. These are this tool's limits. It uses integer arithmetic on the decimal text instead of first converting the input to a floating-point number.
Is this a text or file converter?
No. This page changes the representation of one numeric value. It does not decode text, interpret file bytes or apply a fixed-width machine-word format. For binary input and a decimal integer result, use Binary to Decimal. That page retains its integer-only reverse mode; this page adds decimal fractions and calculation steps. For octal output use Decimal to Octal; for hexadecimal integer input use Hex to Decimal.
Do I need an account or upload anything?
No. Calculation and copying run locally in your browser. There is no batch mode or saved conversion history, and the tool does not transmit your input.
For binary numbers grouped directly into octal digits, use Binary to Octal.