Question: 8. The output (\mathrm{Y}) of the given logic implementation is similar to the output of an/a \_\_\_\_ gate.
(1) AND
(2) NAND
(3) OR
(4) NOR
Answer: Option (4)
Explanation:
Each of the first two gates in the circuit is a NOR gate, because both have an OR gate symbol with a small circle (representing negation) at the output.
1. For the upper NOR gate, the inputs are A and B. The output is
\overline{A + B}.2. For the lower NOR gate, the inputs are A and A. The output is
\overline{A + A} = \overline{A}.3. These two outputs go into an OR gate. So the final output Y is
Y = \overline{A + B} + \overline{A}.4. Simplify the expression:
\overline{A + B} = \overline{A}\,\overline{B}(using De Morgan’s law)
Thus,
Y = \overline{A}\,\overline{B} + \overline{A} = \overline{A}(\overline{B} + 1).Since (\overline{B} + 1) = 1, we get
Y = \overline{A}.5. The output \overline{A} is exactly the output of a NOR gate with both inputs as A, i.e., a NOT operation.
Hence the overall function behaves like a NOR gate.