Evaluate the Boolean expression A⊕A’
Understand the Problem
The question asks to evaluate the Boolean expression A⊕A’, which involves the XOR operation between a variable A and its negation A’. The XOR (exclusive OR) operation results in true if one of the operands is true and the other is false.
Answer
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Answer for screen readers
The expression $A \oplus A'$ evaluates to 1.
Steps to Solve
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Identify the Variables and Operations In this case, we have the variable $A$ and its negation $A'$. We also need to understand the XOR operation, which is represented by the symbol $\oplus$.
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Understand the Truth Values Recall the truth values of $A$ and $A'$. The possible values for $A$ are
true(1) andfalse(0). Therefore, if $A$ is 0, then $A'$ is 1, and vice versa. -
Evaluate the XOR Operation We can evaluate the expression $A \oplus A'$ using the rule of XOR, which states that $A \oplus B = 1$ if $A \neq B$, and $A \oplus B = 0$ if $A = B$.
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Check Both Cases
- If $A = 0$: Then $A' = 1$ and $A \oplus A' = 0 \oplus 1 = 1$.
- If $A = 1$: Then $A' = 0$ and $A \oplus A' = 1 \oplus 0 = 1$.
- Conclusion In both cases, we see that the result of $A \oplus A'$ is always 1.
The expression $A \oplus A'$ evaluates to 1.
More Information
The expression $A \oplus A'$ will always yield true regardless of the truth value of $A$, because a variable and its negation will always be different from each other. This reflects one of the important properties of the XOR operation.
Tips
Sometimes, students may forget the basics of the XOR operation and assume that it behaves like a normal OR operation. Remember that XOR outputs true only when the inputs are different.
