Draw a logic diagram and equations for the following problem.

Consider a traffic light with 3 stages, red green and yellow. The timer starts at 0000, and increments by 1 every clock cycle. The timer goes back to 0000 every time it reaches 15. This timers value is used to determine the light state. At the start when timer = 0000 the light is red and it stays red while it is < 3, when timer =3 the light transitions to green. when 3<=timer<12 it stays green and when 12 <=timer<15 the timer is yellow when timer=15 it goes back to 0000. At any time the input "reset" will reset the timer back to 0. To represent the 3 colors there is a 2 bit output where red = 00, yellow = 01, and green = 10, along with the 4 bit timer output.