Binary Calculator
Perform arithmetic on binary numbers, with results shown in binary, decimal, hexadecimal, and octal, plus conversions of each input.
Result
10000
16
0x10
0o20
10000
How the Binary Calculator Works
This calculator lets you perform arithmetic directly on binary (base-2) numbers. Enter two binary strings using only 0s and 1s, choose an operation, and the result is shown in binary, decimal, hexadecimal, and octal — along with a decimal conversion of each input for reference.
Binary arithmetic follows the same rules as decimal, but carries happen at 2 instead of 10. The calculator converts your inputs to integers internally, performs the operation, and converts back to all common bases.
Example
1010 (binary for 10) + 110 (binary for 6) = 10000 (binary for 16). In hex: 0xA + 0x6 = 0x10. In octal: 0o12 + 0o6 = 0o20.
Common Use Cases
- Learning how binary arithmetic works in computer science courses.
- Verifying manual binary addition, subtraction, multiplication, or division.
- Quick conversion between binary, decimal, hex, and octal representations.
- Debugging bitwise operations in programming.
FAQs
What if I enter invalid binary digits?
Only 0s and 1s are valid in binary. If you enter other digits (like 2 or 3), they will be ignored and the result will reflect only the valid binary digits in order.
Can I divide binary numbers?
Yes — division is supported. If the result is not a whole number, the decimal value is shown (e.g. 1010 ÷ 11 = 11.1 in binary, which is 10 ÷ 3 ≈ 3.3333 in decimal).
Why show the result in multiple bases?
Different bases are useful in different contexts: binary for low-level computing, hex for memory addresses and color codes, octal for Unix file permissions, and decimal for everyday use.