Problem 1: Consider the following characteristic function of a 1-flip-flop circuit with inputs X,Y. (20 points) Here Q=Q(t) is the current value of the flip-flop output and Q=Q(t+1) is the next value of the flip-flop output. (a) Derive a characteristic equation for the above table. (b) Draw a state diagram for the above table. Use minimized transition expressions to label the arrows in your state diagram. (c) Write Verilog code for the one flip-flop circuit