Consider a combinational digital circuit consisting of three inputs (x, y and z) and four outputs (F, G, H and J). Note that each output is a function of all the inputs. These functional relationships are described by: F(x,y,z) = xyz + xyz + xyz + xyz G(x,y,z) = xy + xz + yz H(x,y,z) = xz + yz + xyz J(x,y,z) = xyz Perform the following steps: (a) Generate one of more truth tables showing the relationships between inputs and outputs.

(b) Generate a circuit diagram (using Logisim) illustrating those relationships and minimizing the number of gates used. (Note that inverters are also considered as gates.)

(c) Use the result of (b) to simulate the circuit using Logisim. Verify that your truth table results are correct. Note that (b) and (c) results can be combined since the same digital circuit is used. Logisim file (.circ) should also be submitted.

(d) Optional (extra credit) Consider F and G outputs as one group, and H and J outputs as another. Can you figure out what practical purpose the outputs of each group might have?