2. Sequence Counter

Using D flip-flops, design a 3-bit binary counter which counts in the following sequence: 0, 2, 4, 1, 3, 5, and the repeats the cycle. Use don't cares for the unused states (110 and 111). Follow the same steps as in the lecture: describe the states, draw the state diagram and the next-state table, provide the expression and then the circuit diagram. In order to receive full credit, you must include the relevant K-maps.

After you have completed your design, answer the following three questions.

Assuming that the counter starts in state 110, which state does the counter enter next?

Assuming that the counter starts in state 111, which state does the counter enter next?

Again assuming that the counter starts in state 111, describe the long-term behavior of the counter.

Hint: Read the counter examples in Lumetta's lecture notes 3.1 and 3.2.