$1.(12$ points$)$ Design a system that outputs the maximum of data input samples. The system has an $8-$bit unsigned data input $\backslash ($ I $\backslash ),$ and an $8-$bit unsigned output $\backslash ($ M A X $\backslash ).$ The data input is sampled when a single bit input $\backslash ($ s $\backslash )$ changes from $0$ to $1.$ In other words, the system notices the current value of $\backslash ($ I $\backslash )$ whenever $\backslash ($ s $\backslash )$ goes from $0$ to $1,$ then outputs the maximum of all the samples received so far. Additionally, the system has a single bit input $\backslash ($ r $\backslash )$ which controls a reset. Whenever $\backslash ($ r$=1\backslash )$ the maximum should be reset to zero.

$($a$)$ Draw an HLSM describes the behavior of the system.

$($b$)$ Draw the data path for the processor.

$($c$)$ Draw the custom processor architecture showing inputs, outputs, and connections for controller and datapath.

$($d$)$ Draw the FSM state diagram for the controller of the processor.

$2.(12$ points$)$ Update the soda dispenser example discussed in class $($and in Chapter $5$ of Vahid$)$ with the following modifications:

$-$ Add a multi$-$bit output $\backslash (($R$)\backslash )$ which denotes the number of cents that should be returned as change. This output should be zero unless the total is greater than the amount for the soda.

$-$ You can assume that when the dispense output is one, the machine will automatically return the amount of change stored in $\backslash ($ R $\backslash ).$

$-$ Add another multi$-$bit input $\backslash (($T$)\backslash )$ which is an alternate cost for the soda $($i$.$e$.$ the soda could cost either $\backslash ($ S $\backslash )$ or $\backslash ($ T $\backslash )).$

$-$ Add a single bit input $\backslash (($b$)\backslash )$ which determines which cost to use. If $\backslash ($ b$==0\backslash ),$ soda costs $\backslash ($ S $\backslash ),$ otherwise it costs $\backslash ($ T $\backslash ).$

$($a$)$ Draw an HLSM which includes new inputs and behaviors.

$($b$)$ Draw the data path for the processor.

$($c$)$ Draw the custom processor architecture showing inputs, outputs, and connections for controller and datapath.

$($d$)$ Draw the FSM state diagram for the controller of the processor. $3.(12$ points$)$ A soda manufacturing plant needs to monitor the amount of carbonated water in two storage vats $($Storage X and Storage Y$).$ Two volume sensors output the volume as $12-$bit numbers. Design a system that will accept the two $12-$bit inputs from the sensors and outputs the following values to a display using a single $12-$bit output:

$-$ Volume in Storage X

$-$ Volume in Storage Y

$-$ Total Volume in Storage X and Storage Y

The amount displayed should depend on a user's button input. Each time a button is pressed the display should cycle to the next option. In other words, the volume displayed will change each time a button input changes from $0$ to $1).$

$($a$)$ Draw an HLSM describes the behavior of the system.

$($b$)$ Draw the data path for the processor.

$($c$)$ Draw the custom processor architecture showing inputs, outputs, and connections for controller and datapath.

$($d$)$ Draw the FSM state diagram for the controller of the processor.