Is XOR associative?
Understand the Problem
The question is asking whether the XOR operation is associative, which means that changing the grouping of the operands does not change the result of the operation. To understand this, we will analyze the properties of the XOR operation and determine if (a XOR b) XOR c is equal to a XOR (b XOR c) for any integers a, b, and c.
Answer
Yes, XOR is associative.
The final answer is yes, XOR is associative.
Answer for screen readers
The final answer is yes, XOR is associative.
More Information
The XOR (exclusive OR) operation is associative, which means the grouping of operands does not change the result. This is because XOR corresponds to addition modulo 2, which is inherently associative.
Tips
A common mistake is confusing XOR with other binary operations that are not associative.
Sources
- Is XOR associative? - quora.com
- Logic Proof of Associative Property for XOR - Stack Overflow - stackoverflow.com
- Useful Properties of XOR in Coding : bitwise manipulation and bitmasking - medium.com
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