Decimal to Binary Converter
Type a base-10 number and get its binary form, with the repeated division steps laid out below.
Binary
| Binary | Decimal | Hex | Octal |
|---|
Going the other way? Use the binary to decimal converter.
To convert decimal to binary, divide by 2 repeatedly, writing down each remainder, until the quotient reaches 0, then read the remainders bottom to top. Converting 13 produces remainders 1, 0, 1, 1, which read in reverse as 1101.
How it works
Every division by 2 peels one binary digit off your number. The remainder can only be 0 or 1, and that is precisely the digit. The first division tells you the ones place, the second tells you the twos place, and so on until nothing is left.
Worked example converting 13:
| Division | Quotient | Remainder |
|---|---|---|
| 13 ÷ 2 | 6 | 1 |
| 6 ÷ 2 | 3 | 0 |
| 3 ÷ 2 | 1 | 1 |
| 1 ÷ 2 | 1 |
The quotient hit 0, so we stop. Reading the remainder column bottom to top gives 1101. Quick check in the other direction: that answer has 1s in the eights, fours, and ones places, and 8 + 4 + 1 is 13. It holds up.
The converter above runs this exact procedure and prints the same table for whatever number you type, along with the hex and octal forms as a bonus. It accepts plain digits, a leading minus sign, and separators like spaces or underscores in long numbers. Results use exact whole-number math, so even very large values convert without rounding. If you want to master the method by hand, including the subtraction shortcut that works top-down, the decimal to binary guide walks through both with practice numbers.
Powers of two to memorize
| Power of 2 | Decimal | Binary |
|---|---|---|
| 2^0 | 1 | 1 |
| 2^1 | 2 | 10 |
| 2^2 | 4 | 100 |
| 2^3 | 8 | 1000 |
| 2^4 | 16 | 10000 |
| 2^5 | 32 | 100000 |
| 2^6 | 64 | 1000000 |
| 2^7 | 128 | 10000000 |
These eight values cover every byte. Knowing them cold makes both directions of conversion much faster.
FAQ
How do I convert decimal to binary?
Divide the number by 2 and write down the remainder, which is always 0 or 1. Divide each new quotient by 2 and keep recording remainders until the quotient reaches 0. Then read the remainders in reverse order. Converting 13 gives remainders 1, 0, 1, 1, which read bottom to top as 1101.
Why do I read the remainders bottom to top?
The first division answers the smallest question, whether the number is odd, and that is the rightmost binary digit. Each later division works out the next place leftward. You collect digits small end first, but numbers are written big end first, so the reading order flips.
When do I stop dividing?
When the quotient reaches 0, not 1. The final line, 1 divided by 2 is 0 remainder 1, produces the leading digit of the answer. Stopping one step early drops that digit and roughly halves your number, which is the most common mistake people make with this method.