$4.(15$ points$)$ Design a digital circuit using

$1.$ two D flip$-$flops to control two different manufacturing processes on the same equipment. The systems engineer has provided the following specification:

The control circuit has two inputs:

E $($Enable$)$

P $($Process Select$)$

and two outputs:

$\backslash (\backslash$mathrm$\{$S$\}\_\{1\}\backslash )($Sequence $1)$

$\backslash (\backslash$mathrm$\{$S$\}\_\{0\}\backslash )($Sequence $0)$

When $\backslash ($ E$=0\backslash ),$ the state of the circuit remains the same.

When $\backslash ($ E$=1\backslash ),$ the circuit outputs will sequence depending on the value of input $\backslash ($ P $\backslash )$ :

When $\backslash (\backslash$mathrm$\{$P$\}=0\backslash ),$ the circuit will go through the transitions from $00$ to $10$ to $11,$ back to $00,$ and then repeats.

When $\backslash ($ P$=1\backslash ),$ the circuit will go through the transitions from $00$ to $11$ to $10,$ back to $00,$ and then repeats.

Use the given signal names for the variables in your solution $($E$,$ P$,\backslash (\backslash$mathrm$\{$S$\}\_\{1\},\backslash$mathrm$\{$~S$\}\_\{0\}\backslash )).$ Do not substitute different variable names.

The flip$-$flop states are the outputs. That is$,$ make the flip$-$flop outputs the circuit outputs.

Use don't$-$care states as appropriate.

Your solution should include a state table and a logic diagram using discrete logic gates.

Be sure to show all your work in arriving at the final logic diagram.