Convert decimal fraction to binary converter
True fractional conversion multiplies the fractional part by 2 repeatedly; this site’s converters work on integers only, so split whole and fractional parts or use a specialized fractional tool.
Detailed answer
For the part after the radix point: multiply by 2, take the integer bit, repeat with the new fraction until it terminates or you stop. Our **Decimal to Binary** page accepts **integer** decimal input only (no decimal point in the value). Use it for the integer portion; for repeating binary fractions, expect to handle the algorithm by hand or with software that supports fixed-point math. Large integers are fine as long as they parse successfully.
Relationship context
Integer radix change is exact; fractional radix change can produce infinite repeating expansions, which is why APIs and calculators often separate integer and fractional handling.
Quick conversion table
| Decimal (input) | Binary (output) |
|---|---|
| 0 | 0 |
| 1 | 0b1 |
| 2 | 0b10 |
| 3 | 0b11 |
| 4 | 0b100 |
| 5 | 0b101 |
| 6 | 0b110 |
| 7 | 0b111 |
| 8 | 0b1000 |
| 9 | 0b1001 |
| 10 | 0b1010 |
| 15 | 0b1111 |
| 16 | 0b10000 |
| Decimal (input) | Binary (output) |
|---|---|
| 11 | 0b1011 |
| 32 | 0b100000 |
| 64 | 0b1000000 |
| 128 | 0b10000000 |
| 256 | 0b100000000 |
| 512 | 0b1000000000 |
| 1024 | 0b10000000000 |
| 2048 | 0b100000000000 |
| 4096 | 0b1000000000000 |
| 8192 | 0b10000000000000 |
| 16384 | 0b100000000000000 |
| 32768 | 0b1000000000000000 |
| 65535 | 0b1111111111111111 |
More Decimal converters
Dedicated pages from Decimal to every other format (binary, octal, decimal, hexadecimal, character), with the same parsing rules as the main Number System Converter.