Question

In the truth table of the above circuit the value of X and Y are

• A. 1,1
• B. 1,0
• C. 0,1
• D. 0,0

Answer 1

The Correct Option is A

Let us analyze the given logic circuit and find the values of \( X \) and \( Y \).

1. First AND Gate:

The first AND gate has inputs \( A \) and \( B \). The output \( E \) will be:

\[ E = A \cdot B. \]

2. Second AND Gate:

The second AND gate has inputs \( A \) and \( E \) (output from the first gate). The output \( X \) will be:

\[ X = A \cdot E = A \cdot (A \cdot B) = A^2 \cdot B. \]

3. First OR Gate:

The OR gate takes inputs \( A \) and \( B \) and gives the output \( Y \):

\[ Y = A + B. \]

Truth Table for \( A \), \( B \), \( E \), \( X \), and \( Y \):

| A | B | E | X | Y |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |

Thus, the values of \( X \) and \( Y \) for \( A = 1 \) and \( B = 1 \) are \( X = 1 \) and \( Y = 1 \). The correct answer is Option (1).