Question

Considering the circuit and the associated signals measured at different pins (numbered as 1, 2, 3, 4, 5) shown in the figure, the correct option is

• A. NOT gate between pins 1 and 2 is faulty.
• B. NOR gate is faulty.
• C. NOT gate between pins 4 and 5 is faulty.
• D. The NOR and output NOT gates, are both faulty.

Hint:

Compute what pin 2, pin 4 and pin 5 should be from \(P\) and \(Q\) using the stated NOT-NOR-NOT chain, then check each measured pin against that expectation to isolate the bad gate.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Write down what each gate is supposed to do if it is working correctly. Pin 2 should be \(P\) inverted (a NOT gate). Pin 4 should be the NOR of pin 2 and \(Q\) (pin 3), that is \(\overline{(\text{pin 2}) + Q}\). Pin 5 (\(Y\)) should be pin 4 inverted (another NOT gate).

Step 2: Key Formula or Approach:
Read \(P\), \(Q\), and pins 2, 4, 5 off the waveform over the six marked time slots, then check each gate's output against what its own inputs demand. Whichever gate's actual output disagrees with the correct logic of its own actual inputs is the faulty one.

Step 3: Detailed Explanation:
Reading the waveform slot by slot (slots 1 to 6):
\(P\): 0, 1, 0, 1, 0, 1.
Pin 2 (measured): 1, 0, 1, 0, 1, 0, which is exactly \(\overline{P}\) in every slot. So the first NOT gate is working correctly.
\(Q\): 0, 0, 1, 1, 0, 0.
Using the correct pin 2 values above, the NOR gate should give \(\overline{(\text{pin }2)+Q}\): 0, 1, 0, 0, 0, 1.
Pin 4 (measured): 0, 0, 1, 1, 0, 0, this is identical to \(Q\) itself, not to \(\overline{(\text{pin }2)+Q}\). The NOR gate's actual output does not match what its own two inputs require, so the NOR gate is faulty.
Pin 5 (measured, \(Y\)): 1, 1, 0, 0, 1, 1, which is exactly the inverse of the (faulty) pin 4 values in every slot. So the output NOT gate is correctly inverting whatever it is handed, it is not at fault.

Step 4: Why the other options are wrong.
Option (A) is wrong because pin 2 matches \(\overline{P}\) perfectly, that NOT gate is healthy.
Option (C) is wrong because pin 5 matches \(\overline{\text{pin 4}}\) perfectly, the output NOT gate is healthy.
Option (D) is wrong because only the NOR stage disagrees with its own inputs, the output NOT gate checks out fine on the (already wrong) signal it receives.

Final Answer:
Both NOT gates behave correctly on their actual inputs; only the middle NOR gate's output fails to match \(\overline{(\text{pin }2)+Q}\). \[ \boxed{\text{NOR gate is faulty}} \]