How to Use XOR Calculator
The XOR Calculator computes the bitwise exclusive OR of two integers. Choose your preferred input base, enter both operands, and the XOR Calculator instantly displays the result in decimal, binary, and hexadecimal, plus a column-aligned bit process diagram.
- Choose Input Base - Select decimal, binary (e.g.
1010), or hexadecimal (e.g.FF) to match the format of your numbers. - Enter Operand A - Type the first number. The placeholder shows an example in the selected base.
- Enter Operand B - Type the second number.
- Read the Result - The XOR Calculator shows A XOR B in decimal, binary, and hex, with a step diagram showing which bits differ.
The built-in truth table reminds you of the core XOR rule: 0⊕0=0, 0⊕1=1, 1⊕0=1, 1⊕1=0.
Formula & Theory - XOR Calculator
The XOR Calculator uses this core formula or rule: the bitwise XOR operation:
A XOR B: for each bit position i,
0 ⊕ 0 = 0
0 ⊕ 1 = 1
1 ⊕ 0 = 1
1 ⊕ 1 = 0
Example:
A = 1 0 1 0 (decimal 10)
B = 0 1 1 0 (decimal 6)
R = 1 1 0 0 (decimal 12)| Symbol | Meaning |
|---|---|
| A, B | Integer operands |
| ⊕ | Bitwise XOR operator |
| A⊕B | Result bit is 1 only if the corresponding bits of A and B differ |
Key identity:
$$A \oplus B \oplus B = A$$
This self-inverse property is what makes XOR valuable in cryptography and error detection.
Assumptions and Limits
The XOR Calculator performs 32-bit unsigned XOR. Results are always non-negative and within the 0–4294967295 range.
Use Cases for XOR Calculator
The XOR Calculator is useful across a wide range of programming, mathematics, and electronics domains:
- Bit manipulation - Toggle specific bits in a value by XOR-ing with a mask.
- Cryptography - One-time pads, stream ciphers, and hash functions all rely on XOR for data mixing.
- Error detection - CRC checksums and parity bits use XOR to detect transmission errors.
- Swap without temp variable - The classic a = a⊕b; b = a⊕b; a = a⊕b swap works because of XOR’s self-inverse property.
- Competitive programming - Many algorithm problems (e.g., find the unique element, subarray XOR queries) require fast mental XOR arithmetic.
- Learning digital logic - The XOR Calculator makes it easy to verify solutions to truth table exercises and gate-level design problems.