Design a clocked synchronous state machine with two inputs, X and Y, and one output, Z. The output should be 1 if the number of 1 inputs on X and Y since reset is a multiple of 4, and 0 otherwise.

1. Create a state and output table with four states: S0, Got zero 1s; S1, Got one 1; S2, Got two 1s; S3, Got three 1s.

2. Create an excitation and output table. Assign the states in binary counting order, i.e. (S0-S3=00, 01, 10, 11).

3. Use Karnaugh maps to obtain the excitation equations and the output equations.