Q$2$: A vending machine for cookies operates as follows.

takes nickels $(5$ cents$)$ or dimes $(10$ cents$).$

No changes are returned.

A cookie costs $15$ cents

input signal: $00($a nickel inserted$),01($a dime inserted$),10($dispense button pressed$),11($not used$)$

output signal: $1($drops a cookie$),0($nothing happens$)$

Note: A cookie drops only when the dispense button is pressed AND the balance is $15$ cents or more. In addition, any remaining balance is forfeited $($no change is returned$)$

$($a$)$ How many states are minimally needed? Answer: $4$

$($b$)$ What is the definition $($meaning$)$ of each state?

Answer: S$0($no balance$),$ S$1($balance $=5c$ balance $=10c$ balance $15c$

$($c$)$ Draw the state diagram. Answer: not provided.

$($d$)$ Construct the state table from $($c$).$ Answer: not provided.

$($e$)$ Derive state equations $($D flip$-$flops and output$)$ from $($d$).$ Be sure to use Kmaps to find simplified equations. Answer: not provided.

$($f$)$ Draw logic diagram from $($e$).$ Answer: not provided.

Note: Drawing rules$/$guidelines of drawing logic diagrams:

On each gate, inputs are placed on the left side while outputs are placed on the right side

Connections lines should be straight lines, running either horizontally or vertically. That is$,$ the lines should not run diagonally or should not be in curve.

Two lines may cross. If connected, place a bullet at the crossing point. That is$,$ two crossing lines without a bullet mark at the crossing point mean two lines are not connected.