Binary Arithmetic Calculator
Add, subtract, multiply, divide, AND, OR, XOR and bit-shift binary numbers, with results in binary and decimal.
Your inputs
Results
Result (binary)
10001
- Result (decimal)
- 17
- Operands in decimal
- 11 and 6
✓Exact calculation — rounded only for display
What this calculator does
Practise or check binary arithmetic and the bitwise operations used in programming, such as AND masks, XOR toggles and shifts, with results shown in both binary and decimal.
Formula and method
Operations on arbitrary-precision integers; division returns quotient and remainder.
Worked example
Calculated by this tool with its default inputs:
Inputs
- First binary number: 1011
- Operation: + add
- Second binary number (or shift amount in binary): 0110
Results
- Result (binary): 10001
- Result (decimal): 17
- Operands in decimal: 11 and 6
How to read the results
Bitwise operations act on each bit position independently.
Assumptions and limitations
- Negative results are shown with a minus sign rather than a fixed-width two’s complement.
Questions
What does a left shift do?
Shifting left by n multiplies by 2ⁿ.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 6 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy