Hardware & Architecture HW #$11100$ Pts $1.$ A Leprechaun will grant you a wish if you are lucky, but if you are unlucky, a Leprechaun will steal your gold. The keys to obtaining luck are knowledge of the Rainbow$$s End location and$/$or possession of a $4$Leaf Clover. The transitions between the states of Lucky and Unlucky are governed by the following rules: $$ If you are in a Lucky State, you will stay in the Lucky State if you have knowledge of the Rainbow$$s End location AND$/$OR if you possess a $4$Leaf Clover. $$ If you are in the Lucky State you will transition to the Unlucky state if you lose track of the Rainbow$$s End location AND you misplace your $4$Leaf Clover. $$ If you are in an Unlucky State, you will remain in the Unlucky State until you find the location of the Rainbow$$s End AND acquire a $4$Leaf Clover. The outputs of the states are Wish Granted or Gold Stolen depending on whether you are Lucky or Unlucky. Let the synchronous Input Signals $$ RE $=1$ Rainbow$$s End Location known RE $=0$ Rainbow$$s End Location not known $4$LC $=1$ Possession of $4$Leaf Clover $4$LC $=0$ No Possession of $4$Leaf Clover Let the synchronous Output Signals $$ WG $=1$ Wish Granted. WG $=0$ No Wish Granted $$ GS $=1$ Gold Stolen GS $=0$ No Gold Stolen There are also asynchronous LUCK OF THE IRISH and CURSE OF THE IRISH signals that will put you in the Lucky or Unlucky state, respectively. a$.(9$ Pts$)$ Complete the given State Transition Diagram. b$.(3$ Pts$)$ Thinking of the Latch as a Finite State Machine, would you classify it as a Mealy type, a Moore type, or a combination of the two. Explain your answer LUCKY WG $=$ GS $=$ UNLUCKY WG $=$ GS $=$ Hardware & Architecture HW #$11100$ Pts c$.(24$ Pts $4$ Pts Per Column$)$ Complete the given State Transition Table d$.(3$ Pts$)$ Derive the Characteristic Next State Equation of the Latch $($Use a K$-$map with the Current State Bits and the Inputs$)$ e$.(6$ Pts $3$ Pts Each$)$ Derive the Output Equations for WG and GS Current State Next State Inputs Outputs Q QNext RE $4$LC WG GS Hardware & Architecture HW #$11100$ Pts $2.$ The Easter Bunny is automating the egg coloring process using an assembly line for applying base color, highlight color, and glitter. The Assembly line contains $0$ to $3$ eggs at any given time. Depending on how efficiently the Easter Bunny can input the eggs into the system. Based on the State Transition Diagram for the Easter egg coloring assembly line is shown below $(1$ Egg, $0$ No Egg$).$ a$.(20$ Pts$)$ Create a State Transition Table based on the State Transition Diagram. b$.(3$ Pts$)$ Is this a Mealy Machine or a Moore Machine? Explain your answer. $000-----0100-----0001-----1010-----0101-----1110-----0011-----1111-----11111111010000000$ Hardware & Architecture HW #$11100$ Pts $3.$ Design a $4-$bit counter with one input $($Start$),$ four negative$-$edge triggered J$-$K flip$-$flops, and basic gates that will count down the $12$ Days of Christmas from $12$ to $1.$ Once the count is at $1,$ it should remain in that state unless the input $$Start$$ is received $($pulse$)$ that will asynchronously restart the counter to $12$ for the next countdown $($Hint: Use the asynchronous Preset and$/$or Clear input to reset the latches when the Start input is received$).$ a$.(16$ Pts$)$ Create the State Transition Table $($Without the Asynchronous restart functionality$)$ b$.(16$ Pts$)$ Determine the simplest expression $($use Karnaugh Maps$)$ for the J and K inputs of each J$-$K Flip$-$Flop. SHOW YOUR WORK.