Output Waveform Y for Given Logic Circuit and Input Waveforms

To determine the output waveform $Y$, we first analyze the given logic circuit and then evaluate its output for each time interval.

1. Analysis of the Logic Circuit

The logic circuit consists of two AND gates and one OR gate:

• The upper AND gate receives input $A$ and the inverted input $\bar{B}$ (indicated by the bubble at its lower input terminal). Hence, its output is: $Y_1 = A \cdot \bar{B}$

• The lower AND gate receives the inverted input $\bar{A}$ (indicated by the bubble at its upper input terminal) and input $B$. Hence, its output is: $Y_2 = \bar{A} \cdot B$

• The outputs $Y_1$ and $Y_2$ are fed into an OR gate to produce the final output $Y$: $Y = Y_1 + Y_2 = A \cdot \bar{B} + \bar{A} \cdot B = A \oplus B$

Thus, the given circuit represents an XOR (Exclusive-OR) gate, which produces an output of $1$ when the inputs $A$ and $B$ are different, and $0$ when they are the same.

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2. Time-Interval Analysis of Inputs and Output

From the given input waveforms of $A$ and $B$:

1. For $0 < t < 1$:

   • $A = 0$
   • $B = 1$
   • $Y = 0 \oplus 1 = 1$

2. For $1 < t < 2$:

   • $A = 1$
   • $B = 0$
   • $Y = 1 \oplus 0 = 1$

3. For $2 < t < 3$:

   • $A = 0$
   • $B = 0$
   • $Y = 0 \oplus 0 = 0$

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3. Conclusion

The output $Y$ is at logic level $1$ for $0 < t < 2$ and at logic level $0$ for $2 < t < 3$. This corresponds to the waveform depicted in Option B.