How to use the decimal to binary converter
- 1Type the number in Decimal (base 10). Commas between thousands are ignored.
- 2Read the result in Binary (base 2). Tick Group digits to split it into groups of four.
- 3Keep Show steps ticked to see each division by 2 and its remainder.
- 4For a negative number as a computer stores it, choose Two's complement under Negative numbers and set the Bit width.
Example
156
Binary: 10011100 Hexadecimal: 9C Octal: 234
156 ÷ 2 = 78 r0, 78 ÷ 2 = 39 r0, 39 ÷ 2 = 19 r1, 19 ÷ 2 = 9 r1, 9 ÷ 2 = 4 r1, 4 ÷ 2 = 2 r0, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1. Reading the remainders from the bottom up gives 10011100.
Division-by-two method
Divide the number by 2, write down the remainder (0 or 1), and repeat with the quotient until it reaches 0. The binary number is the remainders read from the last to the first.
| Division | Quotient | Remainder |
|---|---|---|
| 10 ÷ 2 | 5 | 0 |
| 5 ÷ 2 | 2 | 1 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
Reading upwards: 10 = 1010. A faster mental method for small numbers is to subtract the largest power of two that fits (10 − 8 = 2, 2 − 2 = 0, so bits 8 and 2 are set).
Large numbers
The converter uses arbitrary-precision integers, so values beyond 2⁵³ (9,007,199,254,740,992), where JavaScript and spreadsheets start rounding, still convert exactly. A number needs ⌊log₂ n⌋ + 1 bits: 255 needs 8, 256 needs 9, and one million needs 20. The helper text under the binary field shows the bit count.
Negative numbers
There are two ways to write −10 in binary:
- Minus sign:
-1010. Fine on paper, but computers don't store a separate sign symbol. - Two's complement: write 10 in the chosen width (
00001010), flip every bit (11110101) and add 1:11110110. This is how processors store signed integers.
The width matters: −10 is 11110110 in 8 bits and 1111111111110110 in 16 bits. If a number does not fit (for example −200 in 8 bits, whose range is −128 to 127), the tool says so instead of wrapping around.
Decimal fractions to binary
For the part after the point, multiply by 2 and take the whole-number part as the next bit, then repeat with what is left:
0.625 × 2 = 1.25 → 1, 0.25 × 2 = 0.5 → 0, 0.5 × 2 = 1 → 1, so 0.625 = 0.101.
Most decimal fractions never finish in binary. 0.1 becomes 0.0001100110011… forever, which is why 0.1 + 0.2 isn't exactly 0.3 in most programming languages. The converter stops after 32 binary places and tells you the result was cut off.
Quick reference: 0-255
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0 | 16 | 10000 |
| 1 | 1 | 32 | 100000 |
| 2 | 10 | 64 | 1000000 |
| 3 | 11 | 100 | 1100100 |
| 4 | 100 | 127 | 1111111 |
| 5 | 101 | 128 | 10000000 |
| 8 | 1000 | 200 | 11001000 |
| 10 | 1010 | 255 | 11111111 |
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