The minimum number of NAND gates required to implement the Boolean function $$A + A\overline B $$ $$ + A\overline B C$$ is equal to

A ROM is to be used to implement the Boolean functions given below:
$${F_1}$$$$(A,\,B,\,C,\,D) = ABCD + \bar A\,\overline B \,\bar C\,\bar D$$
$${F_2}(A,\,B,\,C,\,D) = (A + B)(\bar A\, + \overline B + C)$$
$${F_3}(A,\,B,\,C,\,D) = \sum {13,15 + \sum {3,5} } $$

(a) What is the minimum size of the ROM required?

(b) Determine the data in each location of the ROM.

The output of the circuit shown in figure is equal to

A switch-tail ring counter is made by using a single D flip-flop. The resulting circuit is a