In the logic circuit shown in the figure, if input A and B are 0 to 1 respectively, the output at Y would be 'x'.
The value of x is ____________.

Solution

Physics sir · 4 steps

Follow each wire from A and B and count the inverters: the two AND inputs are always opposite.

1. Trace the wires. B passes through one NOT to give B̄. That signal feeds the NAND and also goes up through a second NOT, so the NOR receives B itself. A goes straight to the NOR, and Ā goes to the NAND.
2. NOR output. With inputs A = 0 and B = 1, the NOR gives 0 + 1̅ = 0. In general this output is A + B̅.
3. NAND output. Its inputs are Ā = 1 and B̄ = 0, so it gives 1 · 0̅ = 1. By De Morgan's theorem this output is Ā·B̄̅ = A + B.

   Y = A + B̅·(A + B) = 0

4. So. The AND gate receives 0 and 1, so Y = 0. A signal ANDed with its own complement is 0 for every input, so x = 0.

The common slip: 1. Missing the second NOT on the B branch sends B̄ = 0 to the NOR, so the NOR gives 1 and Y comes out as 1 instead of 0.

The idea to keep. Two NOTs in series cancel, so trace every inverter on the path carefully. Use De Morgan's theorem to reduce the circuit, and look for a signal meeting its own complement at an AND (0) or an OR (1).

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