A logic network has two data inputs $$A$$ and $$B,$$ and two control inputs $${C_0}$$ and $${C_1}$$. It implements the function $$F$$ according to the following Table.

Implement the circuit using one $$4$$ to $$1$$ Multiplexor, one $$2$$-input Exclusive $$OR$$ gate, one $$2$$-input $$AND$$ gate, one $$2$$-input $$OR$$ gate and one Inverter.

Find the minimum sum of products form of the logic function
$$f\left( {A,B,C,D} \right) = \sum d \left( {3,11,12,14} \right)$$
Where $$m$$ and $$d$$ denote the minterms and don't cares respectively.

Find the minimum product of sums of the following expression
$$f = ABC + \overline A \,\overline B \,\overline C .$$

Show with the help of a block diagram represent Boolean function:
$$f=AB+BC+CA$$ can be realized using only $$4:1$$ multiplexer.