The state table for a 3-bit twisted ring counter is given in Table 4-15. This circuit has no inputs, and its outputs are the uncomplemented outputs of the lip- lops. Since it has no inputs, it simply goes from state to state whenever a clock pulse occurs. It has an asynchronous reset that initializes it to state 000.

(a) Design the circuit using D lip- lops and assuming that the unspeciied next states are don’ t- care conditions.

(b) Add the necessary logic to the circuit to initialize it to state 000 on power- up master reset.

(c) In the subsection “Designing with Unused States” of Section 4-5, three techniques for dealing with situations in which a circuit accidentally enters an unused state are discussed. If the circuit you designed in parts (a) and (b) is used in a child’s toy, which of the three techniques given would you apply? Justify your decision.

(d) Based on your decision in part (c), redesign the circuit if necessary.

(e) Repeat part (c) for the case in which the circuit is used to control engines on a commercial airliner. Justify your decision.

(f) Repeat part (d) based on your decision in part (e).

Table 4-15:

State Table for Problem 4-29 Next State ABC Present State ABC 000 100 110 111 011 001 100 110 111 011 001 000