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GATE CSE 2025 Session 2 Q31: Output of a NAND, NOT, AND and OR gate circuit

Question

Consider the following logic circuit diagram.

Inputs Y and X feed a NAND gate; X feeds a NOT gate; X and NOT Y feed an AND gate; the three gate outputs go into an OR gate whose output is F
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Which is/are the CORRECT option(s) for the output function FF?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
Show answer and explanation

Answer: A, B, C (official GATE 2025 final answer key)

Concept used: Read the gate expressions off the diagram, then simplify with absorption and De Morgan's law.

First step: The OR gate receives XY‾\overline{XY}, Xˉ\bar{X} and XYˉX\bar{Y}; both Xˉ\bar{X} and XYˉX\bar{Y} are already covered by XY‾=Xˉ+Yˉ\overline{XY} = \bar X + \bar Y.

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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