Design a circuit with input p and output f that will output f = 1 if the past three inputs (not including the current input), formed either 010 or 000. Otherwise, f = 0. Note: This is a Moore-type finite-state machine. (a) Construct the state diagram. (b) Construct the state table. (c) Specify a state assignment, and construct the state-assigned table. (d) Use the Karnaugh map to derive minimal Boolean expressions for the next state variables and the output f. Show your derivation. (e) Plot your final circuit design