3.2 On-Off switch, with synchronous Reset We consider the On-Off Switch that is operated by means of a single push-button, as presented during the Lectures. Recall that this required a finite automaton with 4 states, which were named A, B, C, and D. In this exercise we will be studying synchronous implementations only, by means of edge-triggered D-Flip- Flops. In the Lectures an implementation has been shown that is based on a state assignment using a Gray code. Now we study the following state assignment, in which successive states just have been numbered 0,1, 2,3, represented in binary, as follows: State A B 1 1 1 1 a) Using this state assignment, construct new truth tables for the output x, and for the new-state values Snew and and tnew .Derive a Karnaugh diagram for each of these three values and write down the resulting Boolean expressions. We now wish to extend the On-Off Switch with an additional input, named r. Whenever r = 0 the Switch behaves exactly as before. When, however, r = 1 the Switch will return to its initial state immediately, that is, at the very first rising clock transition after r has become 1. (So, just as is the case with p, the responses of the circuit to r occur synchronously with the clock.) As long as r = 1 the Switch will remain in its initial state, so as long asr = 1, the value of input p is irrelevant. b) Construct a new State-Transition diagram for this extended On-Off Switch. c) Using the state assignment given above, construct new truth tables for the output x , and for the new- state values snew and and tnew .Derive a Karnaugh diagram for each of these three values and write down the resulting Boolean expressions. d) Draw a circuit diagram that implements this automaton, using edge-triggered D-Flip-Flops for the state variables. e) Simulate this circuit. Test it with a simulation frequency of 1ms and an oscillator half-step of 1000 : How responsive is this circuit to input changes? Test it with an oscillator half-step of clock frequency of 500 : How responsive is the circuit now? Determine experimentally what is the smallest half-step value such that, to a human observer, the circuit appears to respond "immediately" to input changes.