Draw the output signal Y in the given combination of gates.

Solution

Physics sir · 3 steps

Reduce the gates to one Boolean expression first, then read the waveforms interval by interval.

1. NAND as NOT. Both inputs of the NAND gate are tied to A, so its output is A · A̅ = A̅. A NAND with its inputs joined is just a NOT gate.
2. Build Y. The OR gate gives A̅ + B, and the final NOT inverts it. By De Morgan's theorem, A̅ + B̅ = A · B̅.

   Y = A̅ + B̅ = A · B̅

   Interval	A	B	Y = A · B̅
   0 to 1 s	1	0	1
   1 to 2 s	1	1	0
   2 to 3 s	0	0	0
   3 to 4 s	1	1	0
   4 to 5 s	1	0	1

3. So. Y is high only from 0 to 1 s and from 4 to 5 s, and low from 1 s to 4 s. That is the waveform in option (a).

The idea to keep. With a gate combination, never trace waveforms gate by gate blindly. Simplify to one expression like Y = AB̅, then check only where it is 1.

Answer from the NTA final answer key. Solution by PrepWiser.