9. Where should the left and right arrows be directed in order that the state diagram illustrated detect the input sequence X = 1011 with overlap?

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

2 is CORRECT. The right arrow represents the good sequence X=1011 which can overlap itself one bit as shown as follows: 

	 1011=good
	    1011=good
Notice that the last bit of the first good sequence overlaps the first bit of the second good sequence. Thus the right arrow should go to state b, which remembers 1 bit of overlap. (If no overlap was required in the later case, the right arrow would go to state a instead). The left arrow represents the bad sequence X=11 which can overlap the good sequence 1 bit as shown here: 
	 11=bad
	  1011=good
Thus, the left arrow should return to state b, since state b remembers one bit of overlap.

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