Let a digital microcontroller, driven by a clock and three inputs A$,$ B and C$,$ produce three outputs X$,$ Y and Z$.$ The microcontroller continuously runs through the following sequence of events: At the start of the first clock cycle, the X line is set to $1.$

At the start of the second clock cycle, line Y or line Z is set to $1,$ depending on whether line A is $1$ or $0,$ respectively, in the previous clock cycle. The microcontroller then waits until the B line becomes $1.$ At the next positive clock edge, the microcontroller examines the C input and if it is $0,$ sets the Z output to $1$ and resets the Z output for two clock cycles, differently sets the Z output signal to $1$ and resets the X and Y outputs for one clock cycle. It then resets all output signals to zero for one clock cycle. This sequence is repeated, starting at the next positive clock edge.

Draw a state diagram and give the next state logic functions and output signals for the above microcontroller.