Consider the circuit shown in the figure.

The Boolean expression F implemented by the circuit isThis question was previously asked in

GATE EC 2017 Official Paper: Shift 2

- \(\bar X\bar Y\bar Z + XY + \bar YZ\)
- \(\bar XY\bar Z + XZ + \bar YZ\)
- \(\bar XY\bar Z + XY + \bar YZ\)
- \(\bar X\bar Y\bar Z + XZ + \bar YZ\)

Option 2 : \(\bar XY\bar Z + XZ + \bar YZ\)

Free

CT 3: Building Materials

2894

10 Questions
20 Marks
12 Mins

F' = X̅.Y + X.0 = X̅.Y

F = Z̅.F' + Z.F̅'

= Z̅.(X̅.Y) + Z.(X̅.Y)' ---(1)

\(\overline{XY}=\overline{X}+\overline{Y}\)

Using the above in Equation (1):

= Z̅.X̅.Y + Z.(X + Y̅)

= X̅YZ̅ + XZ + Y̅Z

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