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

Answer: (A)

1,1

Answer 2

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).