Semiconductors

JEE Main level, single correct, medium

132 of 209

Question 132 of 209

If XX and YY are the inputs, the given circuit works as _______.

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Answer: (D) NOR gate

The circuit consists of four NAND gates.

The first two NAND gates have their inputs tied together, acting as NOT gates. Their outputs are X‾\overline{X} and Y‾\overline{Y}.

These outputs are fed into the third NAND gate. The output of this gate is:
y′=X‾⋅Y‾‾y' = \overline{\overline{X} \cdot \overline{Y}}

Using De Morgan's theorem:
y′=X‾‾+Y‾‾=X+Yy' = \overline{\overline{X}} + \overline{\overline{Y}} = X + Y

This output is fed into the fourth NAND gate, which also has its inputs tied together, acting as a NOT gate. The final output is:
Output =X+Y‾= \overline{X + Y}

This represents the Boolean expression for a NOR gate.

Answer: NOR gate

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