Question

The output of the circuit is low (zero) for:

(A) \( X = 0, Y = 0 \) 
(B) \( X = 0, Y = 1 \) 
(C) \( X = 1, Y = 0 \) 
(D) \( X = 1, Y = 1 \) 
Choose the correct answer from the options given below:

• A. (A), (B) and (C) only
• B. (B), (C) and (D) only
• C. (A), (C) and (D) only
• D. (A), (B) and (D) only

Hint:

In an AND gate, the output is 1 only when both inputs are 1. In an OR gate, the output is 1 if at least one input is 1. Consider these truth tables when analyzing circuits.

Answer 1

The Correct Option is A

The given circuit consists of two logic gates:

• The first gate is an AND gate.
• The second gate is an OR gate.

Let's evaluate the output for each pair of \( X \) and \( Y \):

• When \( X = 0 \) and \( Y = 0 \), the output of the AND gate is \( 0 \) because both inputs are zero. The output of the OR gate is also \( 0 \), since the OR gate only outputs 1 when at least one input is 1. Thus, the final output is low (zero).
• When \( X = 0 \) and \( Y = 1 \), the output of the AND gate is \( 0 \). The OR gate outputs \( 1 \), but since the AND gate's output is zero, the final output is still low.
• When \( X = 1 \) and \( Y = 0 \), the output of the AND gate is \( 0 \) because the second input is zero. The OR gate outputs \( 1 \), but the final output will still be low.
• When \( X = 1 \) and \( Y = 1 \), the AND gate outputs \( 1 \), and the OR gate also outputs \( 1 \), resulting in a high output.

Thus, the output is low for the following combinations:

• (A) \( X = 0, Y = 0 \)
• (B) \( X = 0, Y = 1 \)
• (C) \( X = 1, Y = 0 \)

Final Answer: (1) (A), (B), and (C) only.

Answer 2

Step 1: Understand the problem setup.
The given circuit has two logic gates: 
1. NAND Gate (on the left) 
2. NOT Gate (on the right) We are asked to find when the output of the circuit is low (0).

Step 2: Understand the behavior of the gates.
- NAND Gate: The output of a NAND gate is high (1) unless both inputs are high (1). If both inputs are high, the output will be low (0). 
- NOT Gate: A NOT gate inverts the input. If the input is high (1), the output is low (0). If the input is low (0), the output is high (1).

Step 3: Determine the output of the circuit.
For the output to be low (0) at the NOT gate, the input to the NOT gate (which is the output of the NAND gate) must be high (1). Therefore, the NAND gate must output 1 for the NOT gate to produce a 0.

Step 4: Analyze the possible cases for \( X \) and \( Y \).
We need to check each case to see when the output will be low (0): 
- Case (A): \( X = 0, Y = 0 \)
The output of the NAND gate is \( \text{NAND}(0, 0) = 1 \).
The output of the NOT gate is \( \text{NOT}(1) = 0 \).
Output is low (0).
- Case (B): \( X = 0, Y = 1 \)
The output of the NAND gate is \( \text{NAND}(0, 1) = 1 \).
The output of the NOT gate is \( \text{NOT}(1) = 0 \).
Output is low (0).
- Case (C): \( X = 1, Y = 0 \)
The output of the NAND gate is \( \text{NAND}(1, 0) = 1 \).
The output of the NOT gate is \( \text{NOT}(1) = 0 \).
Output is low (0).
- Case (D): \( X = 1, Y = 1 \)
The output of the NAND gate is \( \text{NAND}(1, 1) = 0 \).
The output of the NOT gate is \( \text{NOT}(0) = 1 \).
Output is high (1).

Step 5: Final Answer.
The output of the circuit is low (0) for the following cases:
- \( X = 0, Y = 0 \) (A)
- \( X = 0, Y = 1 \) (B)
- \( X = 1, Y = 0 \) (C)
Thus, the correct answer is:
 

(A), (B) and (C) only