Decimal to Binary Converter
Convert decimal numbers (base 10) to binary (base 2) with division-by-2 remainder working shown.
How to use it
- Enter a standard decimal number to get its binary equivalent.
Examples
| 10 | 1010 |
| 255 | 11111111 |
Decimal (base 10) is the counting system almost everyone learns first — ten digits, 0 through 9. Binary (base 2) uses only 0 and 1, and is how every digital circuit ultimately represents numbers. Converting decimal to binary means re-expressing a value as a sum of powers of 2.
The standard method is repeated division by 2: divide the number by 2, record the remainder (0 or 1), then divide the quotient by 2 again, and keep going until the quotient reaches 0. Reading the remainders bottom-to-top gives the binary number.
Worked example
10 ÷ 2 = 5 remainder 0. 5 ÷ 2 = 2 remainder 1. 2 ÷ 2 = 1 remainder 0. 1 ÷ 2 = 0 remainder 1. Reading remainders bottom to top: 1010.
255 converts to 11111111 — eight 1s, because 255 is one less than 256 (2⁸), the largest value that fits in a single 8-bit byte.
Where this comes up
- Computer science homework and technical interviews that test number-base fluency
- Working out subnet masks, bit flags or register values by hand
- Understanding how a familiar decimal number — a file size, a port number, a color value — is stored at the hardware level
Last updated 18 August 2026