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: Write the ideal output as a single function of $P$ and $Q$.
If every gate worked, $Y = \overline{\overline{\overline{P}+Q}} = \overline{P}+Q$ (inverting a NOR twice just gives back the OR of its inputs). So a fully healthy circuit should give $Y=\overline{P}+Q$ directly from $P$ and $Q$, regardless of what happens at the intermediate pins.

Step 2: Compute this ideal $Y$ from the given $P,Q$ waveform.
Reading $P$: 0,1,0,1,0,1 and $Q$: 0,0,1,1,0,0 across the six slots, $\overline{P}$ is 1,0,1,0,1,0, so $\overline{P}+Q$ is:
slot1: $1+0=1$, slot2: $0+0=0$, slot3: $1+1=1$, slot4: $0+1=1$, slot5: $1+0=1$, slot6: $0+0=0$.
Ideal $Y$ = 1, 0, 1, 1, 1, 0.

Step 3: Compare with the measured $Y$ (pin 5).
The measured pin 5 trace reads 1, 1, 0, 0, 1, 1, which disagrees with the ideal 1, 0, 1, 1, 1, 0 in slots 2, 3, 4 and 6. Since the fully-correct circuit and the actual circuit disagree, at least one gate must be broken; now isolate which.

Step 4: Isolate the faulty gate using the intermediate pins.
Pin 2 measured is 1,0,1,0,1,0, which equals $\overline{P}$ exactly, so gate 1 (the input NOT) is fine.
Pin 4 measured is 0,0,1,1,0,0, but $\overline{(\text{pin }2)+Q}$ works out to 0,1,0,0,0,1, so the NOR gate's output does not match its own inputs, this is the broken stage.
Pin 5 measured, 1,1,0,0,1,1, is exactly $\overline{\text{pin 4 (measured)}}$, so the last NOT gate is correctly inverting the bad signal it was handed; it is not itself broken.

Step 5: Confirm against the options.
Since the mismatch traces back to the NOR stage alone, with both NOT gates verified healthy, the answer is that the NOR gate is faulty.

Final Answer:
Comparing the ideal $Y=\overline{P}+Q$ against the measured waveform, and then checking each pin in turn, pins the fault on the NOR gate. \[ \boxed{\text{NOR gate is faulty}} \]