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

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