Consider the following Boolean function with four variables
$$F\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {1,\,3,\,4,\,6,\,9,\,11,\,12,\,14} \right)} $$ the function is

The control signal functions of a $$4$$-bit binary counter are given below $$($$where $$X$$ “don’t care”$$):$$

The counter is connected as follows:

Assume that the counter and gate delays are negligible. If the counter starts at $$0,$$ then it cycles through the following sequence:

How many $$3$$ to $$8$$ decodes with an enable input are needed to construct to constant $$6$$ to $$64$$ line decoder without using any other logic gates

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $$n$$ variables. What is the minimum size of the multiplexer needed?