The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is:
$$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\limits^ \bullet \left( t \right)} \cr } } \right] = \left[ {\matrix{ 1 & 2 \cr 2 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] + \left[ {\matrix{ 1 \cr 2 \cr } } \right]u\left( t \right) \cr & y\left( t \right) = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] \cr} $$

The Boolean expression $$AB + A\overline C + BC$$ simplifies to

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 output expression for the Karnaugh map shown below is