Answer the following:

a$)$ Use the implication table method to perform state minimization on the

following original FSM and produce the reduced FSM state table:

$[$continued on next page$]$

Homework $7$

b$)$ Determine the output sequence for the original and reduced machines for the

input sequence $100100101011,$ assuming both machines start in state A $.$

If both machines, the original one and the reduced one, are equivalent, then

they should both yield the same output sequence for the same input

sequence. Thus the purpose of this part is for you to verify $($at least

partially"$)$ that the two machines, the original one and the reduced one, are

identical in terms of their output performance. $($ A complete verification

showing equivalency of the two machines may require a more carefully

designed, perhaps longer, input sequence; however, you should consider

that the input sequence used for verification purposes in this part is of

sufficient depth to provide full verification coverage.$)$

Note that the machine under consideration here is a sequence detector; in

this particular problem, the machines should both produce an output of $1$

whenever the input sequence $010$ is applied. You should thus keep this in

mind as you are generating your output sequences for the two machines,

both original and reduced, and use the expected output behavior of this

particular sequence detector as a guide to indicate whether you are doing

everything correctly or not.

c$)$ What is the minimum number of flip$-$flops needed to implement the original

FSM$?$

What is the minimum number of flip$-$flops needed to implement the reduced

FSM$?$

Note that both of the minimum flip$-$flop counts you report should be

integer$-$valued; e$.$g$.,$ there is no such thing as $4\mathrm{.}3$ flip$-$flops $(!).$

Make it really easy for me to find both of your numerical, integer$-$valued

answers to this part.

Also make it really easy for me to distinguish which value corresponds to

the original FSM and which value corresponds to the reduced FSM$.$

Show your work... I would appreciate if it was handwritten and steps were explained and demonstrated