Design a counter circuit that has 2 inputs X and Y, and one output Z by using one-hotstate encoding. Dont draw the circuit diagram.

When X=1, the circuit counts up or down based on the value of Y; when X=0, the circuit remains in its previous state regardless of the value of Y. When Y=1, the circuit changes states upwards in the order given below and continues this way in a loop. When Y=0, the circuit changes states downwards in reverse order and continues this way in a loop. When the circuit counts upwards, the Z output is 1.

The count order for students : 0, 1, 3, 2