$[30$ pts$.]$ Your task is to design a circuit that can grade a multiple$-$choice exam. Here, assume that:

a$.$ There are $16$ students who are taking the exam.

b$.$ The exam has $7$ questions, each worth $1$ point.

c$.$ Each question has choices A$,$ B$,$ C$,$ or it can be left blank $(4$ possibilities$).$

d$.$ There is no negative scoring for selecting the wrong choice and hence, the total score is an integer between $0($leaving all questions blank$)$ to $7($answering all questions correctly$).$

Your task is to compute the total score for each student based on their exam. Draw the HLSM$,$ the datapath and the controller FSM $($not including the circuit$)$ for this.

Hint: You may assume that you have access to three register files $($RF$)$:

An RF of size $1614$ that stores the students' answers $(16$ registers corresponding to $16$ students, each register has $14$ bits, storing the $2-$bit encoded response $($corresponding to which of the $4$ possibilities was selected by the student$)$ for each of the $7$ questions.

An RF of size $72$ which has the correct solutions stored in it for the $7$ questions.