For the expression P = X + XY , how many gates are required for its implementation ?

Options

A. 2
B. 1
C. 3
D. None of the above

Answer

To determine how many gates are required for the implementation of the expression \( P = X + XY \), we can follow these steps:

### Step 1: Analyze the Expression
The given expression is:
\[ P = X + XY \]

### Step 2: Factor the Expression
We can factor out \( X \) from the expression:
\[ P = X(1 + Y) \]

### Step 3: Simplify Using Boolean Algebra
In Boolean algebra, we know that:
\[ 1 + Y = 1 \]
This is because in Boolean logic, any variable ORed with 1 results in 1.

### Step 4: Substitute Back into the Expression
Substituting back into the expression gives:
\[ P = X \cdot 1 \]
Which simplifies to:
\[ P = X \]

### Step 5: Determine the Gates Required
Since \( P \) simplifies to just \( X \), we do not need any logic gates for this implementation. We can simply connect \( P \) directly to \( X \) using a wire.

### Conclusion
Thus, the number of gates required for the implementation of the expression \( P = X + XY \) is **0**.

### Final Answer
The correct option is **D: 0 gates required**.

---