Bitwise XOR Calculator
Compute bitwise XOR (^) to toggle bits, compute parity, and implement basic encryption. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.
Enter binary or decimal numbers.
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Bitwise XOR Calculator?
The Bitwise Exclusive OR operator (XOR, denoted ^ or ⊕) outputs 1 if and only if the input bits are different. If both bits are identical (both 0 or both 1), the result is 0.
How Does It Work?
Apply XOR truth table: 0 ^ 0 = 0, 0 ^ 1 = 1, 1 ^ 0 = 1, 1 ^ 1 = 0. A unique property is that X ^ X = 0 and X ^ 0 = X, making XOR fully self-reversing: (A ^ B) ^ B = A.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- Output is 1 when inputs differ; 0 when inputs are equal.
- Self-inverting: applying the same XOR mask twice restores the original value.
Practical Applications in Engineering
- XOR cipher encryption and one-time pad cryptosystems.
- Toggling bit states without conditional statements (flags ^= MASK).
- XOR swap algorithm (swapping two variables without a temporary buffer).
Common Mistakes to Avoid
- Caution: Confusing bitwise XOR (^) with exponentiation in programming languages (e.g. in Python/C, ^ is XOR, not power).
- Caution: Thinking 1 ^ 1 equals 1.
Frequently Asked Questions
Why is XOR used in encryption and RAID storage?
Because XOR is completely reversible: if C = A ^ B, then A = C ^ B. In RAID 5, parity data is calculated with XOR, allowing any missing drive to be reconstructed.
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