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In this problem, we are given a 4 state transition
diagram.

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We know that it represents a Moore machine
because the output is a function of only the

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current state.
We are also given a partially filled out truth

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table and our first job is to fill in the
missing entries in the truth table.

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In order to do this, we need to find the correlation
between states A -- D and their S1S0 encoding.

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We begin by looking at the output column.
We know that only state A has an output of

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1, so state A's encoding must be 00 and OUT=1
regardless of the input because it is a Moore

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machine.
We also know that from state A on a 1 input,

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the FSM moves to state B.
According to the truth table from state 00

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(which is A), on a 1 input, we move to state
01.

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That means that state B's encoding is 01.
We continue in this manner, now following

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the transitions from state B.
According to the diagram, when IN = 0, we

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move to state D.
So looking up that transition in our truth

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table, tells us that state D's encoding is
10.

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We also see in our state diagram that starting
at state B when IN=1, we move back to state

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A which we now know to be 00.
So we can fill in the next missing entry in

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our truth table.
Now that we have determined the encoding for

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states A, B, and D.
We know that the remaining encoding is for

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state C and that is 11.
At this point, we have all the information

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we need to complete filling out the missing
entries in the truth table.

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Looking at the row where the current state
is 10 (state D) and IN = 1 and the corresponding

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transition in the state diagram, shows us
that in this case we go back to state D.

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Since the encoding of state D is 10, the S0'
entry is 0.

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Because this is a Moore machine, we also know
that the output associated with current state

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D, regardless of the input, is 0, so the missing
output entry is 0.

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Finally, from state 11 (which is state C),
when IN = 1, we see from the state diagram

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that we transition to state A which is state
00, so the remaining missing S0' value is

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0.
We now want to determine whether or not there

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are any equivalent states in this FSM.
In a Moore machine, equivalent states have

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the same output, and the same input transitions.
This rules out state A because it is the only

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one that has a 1 output.
Taking a closer look at states B, C, and D,

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we can see that both states B and C transition
to state D on a 0 input, and to state A on

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a 1 input.
In addition, the output value is 0 for both

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of them.
This means that states B and C are equivalent

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and can be merged into 1 to turn this into
a 3 state FSM.