A sequential system has a binary input and a three-valued output. The output is 0 if the pattern 0110 has not occurred in x(0,t); it has value 1 if the pattern 0110 has occurred but the pattern 1001 has not; and it has value 2 if both 0110 and 1001 have occurred. Give a state description and show the output and the state sequence for the input sequence 0010111011001010. Hint: Decompose the system into two pattern recognizers. Note that the pattern is recognized in the sequence x(0,t) and x(t-3, t) not.