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Working directly with binary arithmetic can be tricky by hand, especially for bitwise operations that don't map cleanly onto familiar base-10 math.
This calculator performs arithmetic and bitwise operations on two binary numbers, converting through decimal and back.
How it works
Enter two binary numbers and choose an operation. The calculator converts both to decimal, performs the chosen arithmetic or bitwise operation, then converts the result back to binary.
- Enter first binary number.
- Enter second binary number.
- Enter operation.
- Click Calculate to see your results.
Examples
1010 + 110
Adding binary 1010 (decimal 10) and binary 110 (decimal 6) gives binary 10000 (decimal 16).
Who should use it
- Checking binary arithmetic for a computer science or digital logic course.
- Understanding how bitwise AND/OR/XOR operations work on specific values.
Industry applications
- Computer science education
- Digital logic and low-level programming
Advantages
- Supports both arithmetic and bitwise operations in one tool.
- Shows the decimal equivalent at every step for easy verification.
Limitations
- Limited to 32-bit binary inputs — very large binary numbers should be handled with a general-purpose big-number tool instead.
Common mistakes to avoid
- Entering a number with digits other than 0 and 1, which isn't valid binary.
- Expecting a two's complement negative result rather than a plain minus-sign representation.
Best practices
- For negative binary results in two's complement form (as used internally by computers), use the site's dedicated Two's Complement Converter after finding the magnitude here.
Tips
- XOR has a useful property: XOR-ing any value with itself always gives 0, and XOR-ing with 0 leaves a value unchanged — properties that make it common in simple checksum and toggle logic.