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What will be the equivalent Boolean expression for X ⊕ Y ⊕ XY, where X and Y are Boolean variables?
- a)0
- b)1
- c)X + Y
- d)XY
Correct answer is option 'C'. Can you explain this answer?
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What will be the equivalent Boolean expression for X ⊕ Y ⊕ XY, where ...
X ⊕ Y ⊕ XY
= X + Y
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What will be the equivalent Boolean expression for X ⊕ Y ⊕ XY, where ...
Explanation:
To find the equivalent Boolean expression for X ⊕ Y ⊕ XY, we need to simplify the given expression by applying the XOR (⊕) operation.
Simplifying the expression:
Let's break down the given expression step by step:
X ⊕ Y ⊕ XY
We can start by applying the XOR operation to X and Y:
X ⊕ Y
Now, let's distribute the XOR operation over the product XY:
(X ⊕ Y) ⊕ XY
Using the XOR identity (A ⊕ A = 0), we can simplify the expression further:
= 0 ⊕ XY
Since the XOR operation with 0 returns the same value, we can simplify it to:
= XY
Explanation of the answer:
The equivalent Boolean expression for X ⊕ Y ⊕ XY is XY.
This means that the output of the expression XY will be the same as the output of X ⊕ Y ⊕ XY.
In other words, the expression XY is equivalent to X ⊕ Y ⊕ XY.
Therefore, the correct answer is option 'C' (XY).
To find the equivalent Boolean expression for X ⊕ Y ⊕ XY, we need to simplify the given expression by applying the XOR (⊕) operation.
Simplifying the expression:
Let's break down the given expression step by step:
X ⊕ Y ⊕ XY
We can start by applying the XOR operation to X and Y:
X ⊕ Y
Now, let's distribute the XOR operation over the product XY:
(X ⊕ Y) ⊕ XY
Using the XOR identity (A ⊕ A = 0), we can simplify the expression further:
= 0 ⊕ XY
Since the XOR operation with 0 returns the same value, we can simplify it to:
= XY
Explanation of the answer:
The equivalent Boolean expression for X ⊕ Y ⊕ XY is XY.
This means that the output of the expression XY will be the same as the output of X ⊕ Y ⊕ XY.
In other words, the expression XY is equivalent to X ⊕ Y ⊕ XY.
Therefore, the correct answer is option 'C' (XY).
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What will be the equivalent Boolean expression for X ⊕ Y ⊕ XY, where X and Y are Boolean variables?a)0b)1c)X + Yd)XYCorrect answer is option 'C'. Can you explain this answer?
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