Decimal to Binary Converter
Type a decimal number and get its binary equivalent instantly, with no practical size limit.
How a decimal number converts to binary
The number is repeatedly divided by 2, noting the remainder (0 or 1) of each division, until it reaches 0; the resulting binary is that list of remainders read bottom to top. This tool does that same calculation using arbitrary-precision arithmetic, not JavaScript's regular number type, so it doesn't lose precision with large numbers.
Step-by-step example: 13 in binary
Dividing 13 by 2 successively and reading the remainders bottom to top (1, 1, 0, 1) gives 1101, which is 13 in binary:
| Division | Quotient | Remainder |
|---|---|---|
| 13 ÷ 2 | 6 | 1 |
| 6 ÷ 2 | 3 | 0 |
| 3 ÷ 2 | 1 | 1 |
| 1 ÷ 2 | 0 | 1 |
If you need to convert between other bases
This page is built specifically for decimal → binary. For binary → decimal, octal, hexadecimal, or any combination between those four bases, use the general number base converter.