a$)$ Using K$-$map, obtain the simplified Boolean expression having a minimum number of literals for the given function $F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}m(1,2,4,5,7,9,11,13,12,15)$

b$)$ Mr$.$ Ramu wants to design a combinational circuit known as LT$3$ with three inputs and one output. The circuit should generate $0$ when the binary input is set to $0,1,2$ and the output is $1$ otherwise.

c$)$ Consider a $5-$bit shift register as given below. Obtain the content of the given register at the end of $5^{th}$ clock pulse. Considering all flip flops are reset to zero and data input D$4$ D$3$ D$2$ D$1$ D$0$ is set to $11010.$