Derive the new next state $($Y$1,$Y$2)$and output $($z$)$equations and draw the circuit diagram.

$(10$ points$)$ Analyzing the effect of different state encodings on the quality of the circuit: In this question,

you will analyze the effect of selecting a different code assignment for states of the machine used in the

previous question. Consider the machine described in the state table in Fig. P$6\mathrm{.}1$ page $417$ in the textbook.

The machine has four states. Let us call them A$,$ B$,$ C$,$ and D$.$ In the figure, Code $00$ corresponds to state A;

$01$ to state B; $10$ to state C; and $11$ to state D$.$ Rewrite the state table with symbolic codes A$,$ B$,$ C$,$ D$.$ Label

the $00$ state as A in ALL the columns, i$.$e$.$ in the present state column as well as in the next state columns.

Similarly, label the states $01$ as B$,10$ as C and $11$ as D$.$

In the previous question you have already derived the logic expressions for the next states and outputs, cor$-$

responding to the above state encodings. Let us now re$-$encode the machine using the following assignments:

$11$ for A; $10$ for B; $00$ for C; and $01$ for D$.$ Re$-$write the state table using the new assignments. Note:

Re$-$assignment of the codes takes place not just in the present states, but also in the next states. Derive the

new next state $($Y$1,$ Y$2)$ and output $($z$)$ equations and draw the circuit diagram. Which code assignment is a

better choice, if the total number of SOP literals is used as the implementation cost $$ the one shown in Fig.

P$6\mathrm{.}1,$ or the one analyzed in this question