Determine Output of Logic Gate Combination for Given Input Pairs

To determine the output $Y$ of the given logic circuit, let us analyze the operation of each gate in the circuit step-by-step:

1. NOT Gate: The input $A$ passes through a NOT gate, giving the output $\bar{A}$.

2. Upper OR Gate: The upper OR gate receives two inputs:

   • Upper input: $\bar{A}$ (output of the NOT gate)
   • Lower input: $B$

   Therefore, the output of the upper OR gate, denoted as $U$, is: $U = \bar{A} + B$

3. Lower AND Gate: Let the output of the lower AND gate be $L$.

4. Final NOR Gate: The rightmost gate is a NOR gate that receives $U$ and $L$ as inputs. The final output $Y$ is given by: $Y = \overline{U + L}$

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Step-by-Step Evaluation for the Given Input Pairs:

Case 1: Inputs $A = 1$ and $B = 1$

1. $\bar{A} = \bar{1} = 0$
2. $U = \bar{A} + B = 0 + 1 = 1$
3. Substituting $U = 1$ into the final output expression: $Y = \overline{1 + L} = \bar{1} = 0$

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Case 2: Inputs $A = 0$ and $B = 1$

1. $\bar{A} = \bar{0} = 1$
2. $U = \bar{A} + B = 1 + 1 = 1$
3. Substituting $U = 1$ into the final output expression: $Y = \overline{1 + L} = \bar{1} = 0$

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Conclusion:

For the given input pairs $(A = 1, B = 1)$ and $(A = 0, B = 1)$, the output $Y$ will be $0, 0$ respectively.

Correct Option: C