Perform arithmetic and bitwise operations on binary numbers. Results are shown in binary, decimal, hexadecimal, and octal.
| Base | Result |
|---|---|
| Binary (2) | 10000 |
| Decimal (10) | 16 |
| Hex (16) | 10 |
| Octal (8) | 20 |
| Decimal | Binary | Hex |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| 10 | 1010 | A |
| 11 | 1011 | B |
| 12 | 1100 | C |
| 13 | 1101 | D |
| 14 | 1110 | E |
| 15 | 1111 | F |
Convert numbers between binary, decimal, and hexadecimal, or perform arithmetic directly on binary values, with our free binary calculator.
Binary (base 2) represents numbers using only 0s and 1s, where each digit's position represents a power of 2. Conversion to decimal sums each binary digit multiplied by its corresponding power of 2.
Computer hardware is built on transistors that have two states (on/off), making binary's two digits (0 and 1) a natural fit for digital electronics.
Since 16 is a power of 2 (2⁴), each hex digit corresponds to exactly 4 binary digits, making conversion straightforward by grouping binary digits in sets of four.
Negative binary numbers are typically represented using two's complement in computing; check if your specific calculation requires signed number handling.
Most calculators handle standard integer ranges; very large numbers may require specialized big-number tools.