The state machine diagram for a synchronous circuit with clock CK for a washing machine is to be developed. The circuit has three external inputs, START, FULL, and EMPTY (which are 1 for at most a single clock cycle and are mutually exclusive), and external outputs, HOT, COLD, DRAIN, and TURN. The datapath for the control consists of a down-counter, which has three inputs, RESET, DEC, and LOAD. This counter synchronously decrements once each minute for DEC = 1, but can be loaded or synchronously reset on any cycle of clock CK. It has a single output, ZERO, which is 1 whenever the counter contains value zero and is 0 otherwise. In its operation, the circuit goes through four distinct cycles, WASH, SPIN, RINSE, and SPIN, which are detailed as follows:
WASH: Assume that the circuit is in its power-up state IDLE. If START is 1 for a clock cycle, HOT becomes 1 and remains 1 until FULL = 1, Filling the washer with hot water. Next, using LOAD, the down-counter is loaded with a value from a panel dial which indicates how many minutes the wash cycle is to last. DEC and TURN then become 1 and the washer washes its contents. When ZERO becomes 1, the wash is complete, and TURN and DEC become 0.
SPIN: Next, DRAIN becomes 1, draining the wash water. When EMPTY becomes 1, the down-counter is loaded with 7. DEC and TURN then become 1 and the remaining wash water is wrung from the contents. When ZERO becomes 1, DRAIN, DEC, and TURN return to 0.
RINSE: Next, COLD becomes 1 and remains 1 until FULL = 1, illing the washer with cold rinse water. Next, using LOAD, the down-counter is loaded with value 10. DEC and TURN then become 1 and the washer rinses its contents.
When ZERO becomes 1, the rinse is complete, and TURN and DEC become 0.
SPIN: Next, DRAIN becomes 1, draining the rinse water. When EMPTY becomes 1, the down-counter is loaded with 8. DEC and TURN then become 1 and the remaining rinse water is wrung from the contents. When ZERO becomes 1, DRAIN, DEC, and TURN return to 0 and the circuit returns to state IDLE.

(a) Find the state machine diagram for the washer circuit.

(b) Modify your design in part (a) assuming that there are two more inputs, PAUSE and STOP. PAUSE causes the circuit, including the counter, to halt and all outputs to go to 0. When START is pushed, the washer resumes operation at the point it paused. When STOP is pushed, all outputs are reset to 0 except for DRAIN, which is set to 1. When EMPTY becomes 1, the state returns to IDLE.