For the logic circuit shown, the output waveform at Y is:

Solution

Physics sir · 3 steps

Each NAND with its inputs joined is just a NOT gate, so the whole circuit turns into a plain OR gate.

1. Shorted NAND. When both inputs of a NAND gate are tied together, the output is A · A̅ = A̅. So the first two gates give A̅ and B̅.

   Y = A̅·B̅̅ = A̅̅̅ + B̅̅̅ = A + B

2. Read the inputs. By De Morgan's theorem the circuit is an OR gate. A is 0 up to t = 2 and 1 after that. B is 1 only from 1 to 2 and after 3.

   Interval	A	B	Y = A + B
   0 to 1	0	0	0
   1 to 2	0	1	1
   2 to 3	1	0	1
   3 to 4	1	1	1

3. So. Y stays low from 0 to 1 and is high from t = 1 onwards. That is waveform (b).

The idea to keep. NAND gates with joined inputs act as NOT gates. Inverting both inputs of a NAND gives an OR gate, so reduce the circuit first and then read the waveform interval by interval.

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