The output waveform of the given logical circuit for the following inputs A and B as shown below, is :

Solution

Physics sir · 3 steps

A NAND with both inputs tied together is just a NOT, so this whole circuit is an OR gate in disguise.

1. Tied NAND is NOT. Each of the first two gates gets the same signal on both inputs. A · A̅ = Ā, so they output Ā and B̄.

   Y = Ā · B̄̅ = Ā̄̄ + B̄̄̄ = A + B

2. Read the inputs. By De Morgan's theorem the circuit is an OR gate. So Y = 0 only when A and B are both 0. Check each interval of the input waveforms.

   Interval	A	B	Y = A + B
   before t₁	0	0	0
   t₁ to t₂	1	0	1
   t₂ to t₃	1	1	1
   t₃ to t₄	0	1	1
   t₄ to t₅	0	0	0
   t₅ to t₆	1	0	1
   after t₆	0	1	1

3. So. The output is 0 before t₁, rises to 1 at t₁, drops to 0 only between t₄ and t₅, and stays 1 afterwards. That is waveform (d).

The idea to keep. Spot the building blocks first: a NAND with tied inputs is a NOT, and a NAND fed by two NOTs is an OR. Then the output is 0 only where both inputs are 0.

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