Binary to Decimal Converter
Type a binary number (only 0s and 1s) and get its decimal value instantly - or type a decimal and get the binary form. The positional logic is what makes it click: each bit is worth double the one to its right, so 1010 is 8+0+2+0 = 10.
This is the foundation under every hex conversion and every bit of computer memory. The converter validates strictly - a stray 2 or a malformed group is flagged rather than silently misread, because in base-2 arithmetic there is no almost.
| Bit position | Value |
|---|---|
| bit 0 (rightmost) | 1 |
| bit 1 | 2 |
| bit 2 | 4 |
| bit 3 | 8 |
| bit 7 (a byte) | 128 |
How to use
- Type a binary number (0s and 1s only) in the first box - the decimal appears instantly.
- Type a decimal number in the second box to get its binary form.
- Try 11111111 and watch it become 255 - the biggest number one byte can hold.
Frequently asked questions
How do you convert binary to decimal?
Each bit is worth a power of 2, doubling right to left: 1, 2, 4, 8, 16... Add the values of the 1-bits. 1101 = 8 + 4 + 0 + 1 = 13. The converter does the sum as you type.
How do you convert decimal to binary?
Divide by 2 repeatedly and read the remainders bottom-up - or subtract the largest power of 2 at each step. The converter uses the same algorithm internally and shows the binary padded to full bytes.
Why do computers use binary?
Two states (on/off, high/low voltage) are physically reliable; ten states are not. Every number, letter and pixel ends up as patterns of bits, which is why binary conversion is CS 101.
What is 2 to the power of 10 in binary terms?
1 followed by ten zeros: 10000000000 binary = 1,024 decimal. That near-thousand is why 'kilo' in computing historically meant 1,024 - the kilobyte that was secretly 1,024 bytes.