Question
Download Solution PDFWhat happens when a bit string is XORed with itself n times as shown below ?
[B ⊕ (B ⊕ (B ⊕ (B ..........n times]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is Remains unchanged when n is even.
Key Points
- When a bit string is XORed (exclusive OR) with itself, the result is always 0.
- For example, if you have a bit string B, XORing B with B will result in 0 (B ⊕ B = 0).
- XOR operation is both associative and commutative, meaning the order of operations does not change the result.
- When the bit string is XORed with itself an even number of times, the result remains unchanged.
- Mathematically, B ⊕ B ⊕ B ⊕ B (n times, where n is even) simplifies to 0 ⊕ 0 = 0.
Additional Information
- The XOR operation is widely used in various fields such as cryptography, error detection, and correction algorithms.
- In computer science, XOR is used in binary addition without carrying.
- When n is odd, XORing the bit string with itself results in the bit string itself (B ⊕ B ⊕ B = B).
- XOR can be used to swap values of two variables without using a temporary variable.
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