Add, mask and convert binary in one place.
Enter two binary numbers, pick an operation, and see the result in binary, decimal, hexadecimal and octal, with a full conversion table for every value.
Your numbers
What this means
Conversion table
| Value | Binary | Decimal | Hex | Octal |
|---|
How binary math works
How Binary Arithmetic Works
Binary (base-2) arithmetic follows the same rules as decimal arithmetic but uses only two digits: 0 and 1. Binary addition carries over when the sum exceeds 1 (1+1=10 in binary). Subtraction, multiplication, and division work similarly. Computers perform all calculations in binary, making it fundamental to digital systems.
Number Base Conversions
This calculator converts results between four number systems: binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8). Hexadecimal is widely used in programming and color codes. Octal was historically important in computing. Understanding conversions between these bases is essential for programmers and engineers.
Common questions
How do I convert binary to decimal?
Each binary digit represents a power of 2, starting from the right. For example, 1010 in binary = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal. This calculator performs the conversion automatically and shows the result in decimal, hexadecimal, and octal.
What if I enter non-binary digits?
Binary numbers should contain only 0s and 1s. If you enter digits other than 0 and 1, the calculator will attempt to parse the input as a binary string. Digits like 2-9 are not valid in binary and may produce unexpected results.
What is the largest binary number I can calculate?
JavaScript handles integers up to 2^53 - 1 (about 9 quadrillion). This means binary numbers up to 53 digits long can be calculated accurately. For most practical purposes, this is more than sufficient.
Bitwise operations (AND, OR, XOR) use 32-bit unsigned integers. Arithmetic is accurate for integers up to 2^53 - 1.