How to convert binary to decimal
Multiply each digit by the base raised to the power of its position (counting from 0 on the right), then add the results.
Example
101101₍2₎ = 1 × 2^5 + 0 × 2^4 + 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 1 × 2^0 = 45About the number systems
Binary
Base 2 uses only the digits 0 and 1. Every value in a computer is ultimately stored as binary; each binary digit is a bit.
Decimal
Base 10 is the everyday number system with digits 0–9; each position is worth ten times the one to its right.
Binary to decimal table
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
| 10000 | 16 |
| 11111 | 31 |
| 100000 | 32 |
| 111111 | 63 |
| 1000000 | 64 |
| 1100100 | 100 |
| 1111111 | 127 |
| 10000000 | 128 |
| 11111111 | 255 |
| 100000000 | 256 |
| 1111101000 | 1000 |
| 10000000000 | 1024 |
| 1000000000000 | 4096 |
| 1111111111111111 | 65535 |
Frequently asked questions
How do I convert binary to decimal?
Multiply each digit by the base raised to the power of its position (counting from 0 on the right), then add the results. Example 101101₍2₎ = 1 × 2^5 + 0 × 2^4 + 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 1 × 2^0 = 45
What is 101101 in decimal?
101101 (binary) = 45 in decimal.
Can I convert very large numbers?
Yes. The converter uses exact big-integer arithmetic, so there is no rounding even for long inputs.