$2$A$)$ Design a sequence detector using Mealy model with one input $Y$ and one output $Z.$ The output $Z$ is

HIGH whenever the sequence $"1001"$ is detected, otherwise the output is LOW. Overlapping of the

sequence is allowed. Implement using JK$-$ flip flops and minimum number of external gates.

$2$B$)$ Realize the Boolean functions:

$F_1(A,B,C)={\displaystyle \underset{m}{\overset{?}{}}}(0,1,2,5)$ and $F_2(A,B,C)=pro{d}_M(1,5,6)$

$2$C$)$ Design a combinational circuit that compares two, $4-$ bit numbers to check if they are equal using

logic gates. The circuit output is equal to $1,$ if the two numbers are equal and $0$ otherwise.