Convert between binary and decimal number systems with this free online calculator. See step-by-step calculations and learn about number conversion.
Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit position represents a power of 2, with the rightmost digit representing 2⁰ (1), the next digit to the left 2¹ (2), then 2² (4), and so on.
Binary Example
Decimal is the base-10 number system we use everyday. It uses ten digits: 0-9. Each digit position represents a power of 10, with the rightmost digit representing 10⁰ (1), the next digit to the left 10¹ (10), then 10² (100), and so on.
Decimal Example
| Binary | Decimal | Hexadecimal |
|---|---|---|
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1001 | 9 | 9 |
| 1010 | 10 | A |
| 1011 | 11 | B |
| 1100 | 12 | C |
| 1101 | 13 | D |
| 1110 | 14 | E |
| 1111 | 15 | F |
To convert a binary number to decimal, multiply each digit by its corresponding power of 2 and add the results.
Formula
Example
| Binary Number | 1 | 1 | 1 | 0 | 0 | 1 |
|---|---|---|---|---|---|---|
| Power of 2 | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰ |