The logical gate implemented using the circuit shown below where $${V_1}$$ and $${V_2}$$ are inputs (with $$0$$ $$V$$ as digital $$0$$ and $$5$$ $$V$$ as digital $$1$$) and $${V_{OUT}}$$ is the output is

The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline B \overline C } \right)$$ can be written as

The Boolean expression $$X\overline Y Z + XYZ + \overline X Y\overline Z + \overline X \overline Y Z + XY\overline Z $$ can be simplified to