(30 pts.) The asynchronous toggle circuit has a single input a and two outputs x and y. Whenever a is low, both outputs are low. The first time a goes high, output x goes high. On the next rising transition of a, output y goes high. On the third rising input, x goes high again. The circuit continues steering pulses on in alternately between x and y. a toggle X a. (4 pts.) Derive the input/output waveform based on the description given above. b. (6 pts.) Provide a primitive flow table for this machine, and reduce the flow table to minimum number of states, if your table is not reduced already. c. (6 pts.) Identify state assignments without critical races, and draw the transition table together with an output table that avoids false outputs. d. (6 pts.) Derive a logic schematic without hazards for the toggle circuit using primitive (AND, OR, inverter) gates. e. (8 pts.) Design the toggle circuit using one or more SR latches. Show the details of your work for full credit.