To convert binary to decimal, write the place values 1, 2, 4, 8, 16 and so on under the bits from right to left, then add the place values that sit under a 1. For 1011 that is 8 + 2 + 1 = 11.
Method: add the place values
Each position in a binary number is worth twice the one on its right. Write the bits, label each with its power of two, and add the ones.
| Binary | Place values used | Decimal |
|---|---|---|
| 1011 | 8 + 2 + 1 | 11 |
| 11010 | 16 + 8 + 2 | 26 |
| 101101 | 32 + 8 + 4 + 1 | 45 |
| 10110101 | 128 + 32 + 16 + 4 + 1 | 181 |
Worked example: 10110101
| Bit | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
|---|---|---|---|---|---|---|---|---|
| Place value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| Counts? | yes | no | yes | yes | no | yes | no | yes |
Add the place values marked yes: 128 + 32 + 16 + 4 + 1 = 181.
Method 2: double and add
Start at 0. For each bit from the left, double the running total and add the bit. For 1011: 0 x 2 + 1 = 1; 1 x 2 + 0 = 2; 2 x 2 + 1 = 5; 5 x 2 + 1 = 11. This is quick to do in your head and never needs a table of powers.
Binary fractions
After the point the place values are 1/2, 1/4, 1/8. So 101.11 is 4 + 1 + 0.5 + 0.25 = 5.75.
Practice problems
Try these, then check against the answers in the table or with the binary to decimal converter.
| Binary | Decimal answer |
|---|---|
| 110 | 6 |
| 1001 | 9 |
| 11111 | 31 |
| 100000 | 32 |
| 1100100 | 100 |
| 11111111 | 255 |
Common mistakes
- Starting the place values from the left instead of the right.
- Forgetting that the rightmost place is 1, not 2.
- Reading leading zeros as part of the value. They add nothing: 00101 is the same as 101.
FAQ
What is 1111 in decimal?
8 + 4 + 2 + 1 = 15.
What is 10000000 in decimal?
A single 1 in the eighth position is 128.
How do I convert a very long binary number?
Use the double-and-add method, or paste it into the converter, which has no length limit.
What about negative binary numbers?
Signed values use two’s complement. See the calculator.