Design Specifications: Design a sequential system that has the following functionality:

a) When the input is x = 0 we see a single red light shifting from left to right, through four different positions in cyclic fashion, with each clock cycle.

b) When the input is x = 1 we see two red lights shifting from left to right, through four different positions in cyclic fashion, with each clock cycle.

c) If the input changes from 0 to 1 or from 1 to 0 in the middle of a cycle the light pattern shifts from one light to two lights or vice versa depending on the previous input and the actual input.

d) Considering the red lights as ones and the other lights as zeros, where the left most bits is taken as the most significant, we want a seven segment display to show the decimal equivalent of the light pattern. If the number is greater than nine it will show the middle segment only.

Design Constraints & Requirements:

1. Do not use more than 4 Flip-Flops of any type.

2. Minimize the use of discrete gates, multiplexers or decoders of any type.