PLEASE DO BY HAND!!!! THANKS

Exercise 5. [10+8+8+8=34 marks] In this exercise we will explore designing an integrated circuit for use within a microwave. Not the whole thing (that's too complex), but just a small piece of it. Consider that the microwave already has a circuit which controls the timer and the magnetron (the thing that produces the microwaves). Your goal is to design a simple circuit which controls the turntable. The turntable is powered by a gear box which takes two input bits: - R. If R1, the gear box rotates. If R0 the gear box does not rotate. - C. If C1 and R1, the gearbox turns clockwise. If C0 and R1, the gearbox turns counterclockwise. The manufacturer of this microwave requests a synchronous circuit which will control the gearbox to alternate between clockwise and counterclockwise rotation each time the microwave is turned on. The circuit to be designed will receive a single input bit I from the circuit controlling the magnetron. - When I1, the turntable should rotate. - When I0, the turntable should not rotate. To guide your design process, complete parts (a) to (d) below. (a) Draw a Finite State Machine which describes this state circuit. Since this circuit has 4 possible combinations of outputs, it should have 4 states. Be sure to include the inputs and outputs in the FSM. Order the outputs as RC. Hence, a transition in the FSM will be labelled as I/RC. The change in direction should be triggered by the microwave turning on. (b) Create a truth table to describe the inputs, outputs, and transitions of your FSM. That is, create a truth table describing the combinational logic of your eventual state circuit. Since there are 4 states, you must have 2 bits of "input" to encode the current state, and 2 bits of "output" to encode the next state. (Hint: your table should have 8 rows and 7 columns.) (c) Give the DNF for each output of the combinational part of your state circuit (there are 4 of them; recall that the "next state" is part of the combinational logic output). Then, simplify each DNF into a reduced sum of products. For this particular question, you do not need to specify the Boolean law being applied at each step of the simplification. (d) Draw a circuit which implements the combinational logic of your turntable controller circuit. That is, draw a circuit implementing your 4 simplified formulas from part (c). Use gates with arity at most 2. For clarity (and to avoid crossing too many lines), you may draw 4 independent circuits, one for each output bit