(Solved): Given \( F(X, Y, Z, W)=\sum m(6,7,12,13) \), a. Write the explicit expression of Fin canonical SOP ...

Given \( F(X, Y, Z, W)=\sum m(6,7,12,13) \), a. Write the explicit expression of Fin canonical SOP form and tally the number of gate inputs (not number of gates). Do not include the NOT gate inputs in the tally. (10 pt) b. Show its K-Map and obtain the simplified SOP form F. Tally the number of gate inputs for the minimized expression. Again do not include the NOT gate inputs in the tally. (10 pt) c. Assign \( X, Y, Z \), and \( W \) to the inputs of the AND-XOR structure, shown below, such that the structure implements \( F(X, Y, Z, W)=\sum m(6,7,12,13) \). Note that the output gate is a two-input \( X O R \) instead of the usual OR. Show your work. ( \( 15 \mathrm{pt} \) ) d. Based on what property of Boolean Algebra can we answer the previous questioni (question 2.c) confidently? (5 pt)