7. Where should the left and right arrows be directed in order that the state diagram illustrated detect the input sequence X = 0011 with no overlap?

  1. Left: a Right: c
  2. Left: b Right: b
  3. Left: b Right: a
  4. Left: c Right: b
  5. Left: c Right: a

5 is CORRECT. The sequence X=0011 cannot overlap itself at all, thus the right arrow should go to state a. The left arrow represents the incorrect sequence X=000, which can overlap the good sequence 2 bits as follows: 

	 000=bad
	  0011=good
Notice that the last 2 bits of the bad sequence can be used as the first two bits of the good sequence. Thus, the left arrow should return to state c, since this state remembers two bits of overlap.

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