A computer game will be designed. Computer will randomly generate a number either $"1"$ or $"2"$ consequently. If the sum of the generated numbers smaller than $2,$ computer continues to generate number. If the sum of the generated numbers exceed $4,$ the game returns to initial state and if the sum is equal to $4,$ the player wins. And game returns to initial state creating an output to score.

a$)$ Draw the state diagram.

b$)$ Fill in the state table

c$)$ Sequential circuit will be implemented using JK type Flipflop. Find the inputs of the T Flipflop after minimizing in Karnough map. Do not draw the circuit.

d$)$ Find the output expression.