How to use the Binary to Decimal Converter
Type a binary number made of 0s and 1s. The decimal value appears along with the hex and octal equivalents.
How binary to decimal conversion works
Each binary digit is a power of two. The rightmost bit is worth 1, the next 2, then 4, 8, 16 and so on. Multiply each bit by its place value and add the results. For 101101 that is 32 + 0 + 8 + 4 + 0 + 1 = 45. A byte has eight places, so its largest value, 11111111, is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
Where you meet binary numbers
Binary shows up in subnet masks, file permissions, bit flags in code, network packets and computer science homework. Converting to decimal makes these values easier to compare and to type into tools that expect ordinary numbers.
The formula
Sum each bit × 2^position.
Examples
- 101101
Decimal: 45 Hex: 2D Octal: 55
- 11111111
Decimal: 255 Hex: FF Octal: 377
- 1000
Decimal: 8 Hex: 8 Octal: 10
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 |
| 100000 | 32 |
| 1000000 | 64 |
| 10000000 | 128 |
| 11111111 | 255 |
Limitations and assumptions
Runs entirely in your browser. Nothing you enter is uploaded.
Frequently asked questions
How do I convert binary to decimal by hand?
Write the place values 1, 2, 4, 8, 16 and so on under the bits from right to left, keep the values that sit under a 1 and add them. 1101 becomes 8 + 4 + 1 = 13.
What is 11111111 in decimal?
255. Eight bits that are all 1 add up to 2⁸ − 1, the largest value an unsigned byte can hold.
What is 1010 in decimal?
10. The two 1 bits stand for 8 and 2, and 8 + 2 = 10.
How do I convert decimal back to binary?
Use the decimal to binary converter, or divide by 2 repeatedly and read the remainders from last to first.