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

To solve the given problem, we need to analyze the logic circuit and determine the output for the inputs \( A = 0, B = 1 \) and \( A = 1, B = 0 \), which correspond to finding \( X \) and \( Y \) in the truth table. Let's break it down step-by-step:

1. Analyzing the Circuit:

• The circuit consists of an AND gate, a NAND gate, and a NOR gate.
• Variables \( X \) and \( Y \) are listed in the truth table for different input values of \( A \) and \( B \).

2. Calculating the Output:

Case 1: \( A = 0, B = 1 \) (Find \( X \))

• AND Gate: The input is \( A = 0, B = 1 \). Output of AND gate is \( A \land B = 0 \land 1 = 0 \).
• NAND Gate: Inputs are \( B = 1 \) and inverted output of AND gate (since NOR gate is connected here), which is 1. Output is: \( \lnot (B \lor 1) = \lnot (1) = 0 \).
• NOR Gate Output \( E/X \): Inputs are \( 0, 0 \). Output is \( \lnot (0 \lor 0) = 1 \).

Thus, for \( A = 0, B = 1 \), the output \( X = 1 \).

Case 2: \( A = 1, B = 0 \) (Find \( Y \))

• AND Gate: The input is \( A = 1, B = 0 \). Output of AND gate is \( A \land B = 1 \land 0 = 0 \).
• NAND Gate: Inputs are \( B = 0 \) and inverted output of AND gate, which is 1. Output is: \( \lnot (0 \lor 1) = \lnot (1) = 0 \).
• NOR Gate Output \( E/Y \): Inputs are \( 0, 0 \). Output is \( \lnot (0 \lor 0) = 1 \).

Thus, for \( A = 1, B = 0 \), the output \( Y = 1 \).

Conclusion:

From the analysis, both \( X \) and \( Y \) are 1 for the respective inputs and configurations. Therefore, the correct answer is 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).