How to convert decimal to binary with steps
Repeatedly divide the integer by 2 and read the remainders from last to first, or subtract the largest power of two until you reach zero.
Detailed answer
For whole numbers: divide by 2, record each remainder (0 or 1), then read the remainders bottom-up. Example: 13 → 1101₂. Our Decimal to Binary converter applies the same integer rules as the hub: enter a decimal value and the tool shows the exact binary string (with optional 0b). For very large integers, use the same page—parsing is integer-only, so fractional decimals are not accepted as a single “decimal fraction” value.
Relationship context
Decimal and binary are two radices for the same integer; switching radix does not change the value, only how it is written. Binary aligns with bit positions, which is why hardware and bitwise logic prefer it.
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.