Conclusion:

    The results of this lab turned out be be very sucessful.  The circuit worked properly and carried the digits as desired.  There was a great amount of theorizing and analysis involved though, for the circuit did not work correctly at first.  It was difficult to weed out the bugs for the problems were not in the state tables nor the diagrams.  They were in the implimentation.
    Upon creating the circuit, both the circuit units to evaluate the output Z and the input for the flip flop D were identical.  This is where I had overlooked the accual values on the state table.  Upon testing the implimentation, both my lab partner and I were puzzled as to why the circuit would not function.
    With some leanthy debugging, I fortunatley came across the algorithm which caused the problem. By realizing that that Z circuit algorithm had been implimented twice, I was able to correct the problem by implimenting the algorithm for the D circuit.  In doing so the implimented circuit for the equation X1 +X2 = Z worked as it should, with the carry unit being retained and reimplimented.