Decimal to Binary Converter
Free online decimal to binary converter. Instantly convert decimal numbers to binary with step-by-step explanation and conversion table.
Convert Decimal to Binary
Enter a decimal (base 10) number and instantly get its binary (base 2) equivalent. Also works in reverse — enter binary to get decimal.
How to convert decimal to binary
Repeatedly divide the decimal number by 2, recording the remainder (0 or 1) each time, until the quotient is 0. Read the remainders from bottom to top to get the binary number.
For example, to convert 13 to binary: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1. Reading remainders bottom to top: 1101.
Decimal to binary conversion table
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
| 32 | 100000 |
| 64 | 1000000 |
| 128 | 10000000 |
| 255 | 11111111 |
| 256 | 100000000 |
| 512 | 1000000000 |
| 1024 | 10000000000 |
Why is binary important?
Binary is the fundamental language of computers. All data — text, images, programs — is ultimately stored and processed as binary digits (bits). Understanding binary is essential for computer science, networking (IP subnets), and low-level programming.