Design a 2-bit binary up/down counter with one input switch X and one output Z using T flip flops. The counter counts as follows: 0,1,2,3,0,1,.. when the input X is ON and the output Z = 1 when the count goes from 3 to 0. The counter counts down as follows: 0,3,2,1,0,3,2... when the input X is OFF and the output Z = 1 when the count goes from 0 to 3. Your design solution must have the following:

1. The state table

2. The state assignment table

3. The excitation table using your choice of flip flops

4. The flip flop input equations and the output equation

5. The final logic diagram ( logic circuit )