How to convert binary to decimal
Each binary digit (bit) represents a power of 2. Starting from the rightmost bit as 20, each position to the left doubles. To convert, multiply each bit by its positional value and sum the results.
Decimal = bn×2n + bn−1×2n−1 + ... + b1×21 + b0×20
Example: 10110101 = 1×128 + 0×64 + 1×32 + 1×16 + 0×8 + 1×4 + 0×2 + 1×1 = 128 + 32 + 16 + 4 + 1 = 181.
Place values reference
| Position | Power | Value |
|---|---|---|
| Bit 0 | 20 | 1 |
| Bit 1 | 21 | 2 |
| Bit 2 | 22 | 4 |
| Bit 3 | 23 | 8 |
| Bit 4 | 24 | 16 |
| Bit 5 | 25 | 32 |
| Bit 6 | 26 | 64 |
| Bit 7 | 27 | 128 |
| Bit 8 | 28 | 256 |
FAQ
What's the biggest binary I can convert?
The converter uses BigInt internally, so there's no practical limit for positive integers.
Can I convert signed (negative) binary?
This tool treats input as unsigned. To represent negatives, use two's complement: for an n-bit number, the most significant bit indicates the sign.
Why does leading zero not change the value?
Leading zeros in any positional number system don't change the value (just as 0123 = 123 in decimal). They only affect the bit-width for sign representation.