Design a sequential circuit which recognizes the sequences 0011 or 1100 on a synchronous input, x. That is, your circuit should have one output signal which is high only when the last 3 inputs and the current input are 0011 or 1100. The output (z) is shown below for a sequence of inputs (x).

x 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 . . . . .z ? ? ? 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 . . . .