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Q. The logic circuit shown below is equivalent toPhysics Question Image

Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

Output of first OR gate is
$A = \left(X+\bar{Y}\right)$
Inputs of second OR gate are $\bar{X}$ and $\bar{A}$.
Output of second OR gate is
$C = \bar{X} +\bar{A}$
$= \bar{X} +\overline{X+\bar{Y}} = \bar{X} +\left(\bar{X}\cdot\bar{\bar{Y}}\right) = \bar{X} +\left(\bar{X}\cdot Y\right)$
$= \bar{X}\left(1+Y\right) = \bar{X}$
Final output is $z = \bar{C} = \bar{\bar{X}} = X$

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