Design a synchronous lighted sign that flashes different colors based on an input L. When L is equal to 0, the sign should flash the following sequence; blue, green, red, and repeat. When L is equal to 1, the sign should flash the following sequence; yellow, off, red, off, yellow, off, red, off, and repeat. Assume the correct color will shine when the associated state is present. If the sign is in the blue or green state and the input L should change to 1, the next state should start the other sequence by transitioning to yellow first. If the sign is in yellow, off, or red states and the input L changes to 0, the next state should start the other sequence by transitioning to blue first.

Create the State Definition Table, State Diagram, Transition Table, combinational logic using Kmaps, and Final Equations assuming JK flip-flops and AND/OR/NOT combinational logic. For any additional binary states that don't exist in your state transition diagram, please solve for the next state using your JK equations and explain what the next state would be if the input was 0 or if the input was 1.