Identification of Equivalent Logic Gate Circuit

To determine the logic gate equivalent of the given circuit, let us analyze the operation of each gate step-by-step.

From the circuit diagram, all four gates are two-input NAND gates.

Step 1: First Stage Gates (Inverters)

1. Top-Left NAND Gate: Both inputs are connected together to signal $X$. The output $A$ of this gate is given by: $A = \overline{X \cdot X} = \overline{X}$

2. Bottom-Left NAND Gate: Both inputs are connected together to signal $Y$. The output $B$ of this gate is given by: $B = \overline{Y \cdot Y} = \overline{Y}$

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Step 2: Second Stage Gate

The middle NAND gate takes $A = \overline{X}$ and $B = \overline{Y}$ as its inputs. The output $C$ of this gate is: $C = \overline{A \cdot B} = \overline{\overline{X} \cdot \overline{Y}}$

Using De Morgan's Theorem ($\overline{P \cdot Q} = \overline{P} + \overline{Q}$): $C = \overline{\overline{X}} + \overline{\overline{Y}} = X + Y$

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Step 3: Final Stage Gate

The output $C = X + Y$ is fed into both inputs of the final NAND gate. The final output of the circuit is: $\text{Output} = \overline{C \cdot C} = \overline{C}$

Substituting $C = X + Y$: $\text{Output} = \overline{X + Y}$

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Conclusion:

The Boolean expression for the output is $\overline{X + Y}$, which represents the operation of a NOR gate.

Correct Answer: NOR gate (Option D)