In the given Boolean expression, `Y=A.bar(B)+B.barA`, if A=1, B=1 then Y will be

Options

A. 0
B. 1
C. 11
D. 10

Answer

To solve the Boolean expression \( Y = A \bar{B} + B \bar{A} \) given that \( A = 1 \) and \( B = 1 \), we can follow these steps:

### Step 1: Substitute the values of A and B
We start by substituting the values of \( A \) and \( B \) into the expression:
\[ Y = A \bar{B} + B \bar{A} \]
Substituting \( A = 1 \) and \( B = 1 \):
\[ Y = 1 \bar{1} + 1 \bar{1} \]

### Step 2: Calculate the complement of B and A
Next, we need to find the complements \( \bar{B} \) and \( \bar{A} \):
- The complement of \( B = 1 \) is \( \bar{B} = 0 \)
- The complement of \( A = 1 \) is \( \bar{A} = 0 \)

### Step 3: Substitute the complements back into the expression
Now we substitute these complements back into the expression:
\[ Y = 1 \cdot 0 + 1 \cdot 0 \]

### Step 4: Perform the multiplication
Now, we perform the multiplication:
\[ Y = 0 + 0 \]

### Step 5: Perform the addition
Finally, we add the results:
\[ Y = 0 \]

Thus, the final value of \( Y \) is:
\[ \boxed{0} \]