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A synchronous state machine has two inputs (X1 and X2) and two outputs (Z1 and Z2). The inputs represent a 2-bit binary number (N). If the present value of (N) plus the previous value of (N) is greater than (2), then (Z1=1). If the present value of (N) times the previous value of (N) is greater than (2). then (22=1). Otherwise, (Z1Z2=00). When the first pair of inputs is received, use (0) as the previous value of (N). The circuit of the aforementioned state machine includes .......... AND-gates