$2)(\backslash (\backslash$mathbf$\{10\}\backslash )$ 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, corresponding to the above state encodings. Let us now re$-$encode the machine using the following assignments: $11$ for $\backslash (\backslash$mathrm$\{$A$\}$ ; $10\backslash )$ for $\backslash (\backslash$mathrm$\{$B$\}$ ; $00\backslash )$ 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 $\backslash (\backslash$left$($Y$\_\{1\},$ Y$\_\{2\}\backslash$right$)\backslash )$ and output $(\backslash ($ z $\backslash ))$ 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?

Figure P$6\mathrm{.}1$ State$-$assigned table for Problems $6\mathrm{.}1$ and $6\mathrm{.}2$