1. Generalized De Morgan’s Theorem Lecture L5.4 Section 5.1

2. What kind of gate is this? X Y Z = X Y !X !Y W Z 0 0 1 1 0 1 X Y Z W !X !Y

3. What kind of gate is this if 0 = TRUE and 1 = FALSE? X Y Z = X Y !X !Y W Z 0 0 1 1 0 1 X Y Z W !X !Y X Y Z 0 = TRUE = T

4. What kind of gate is this? X Y Z = X Y !X !Y W Z 0 0 1 1 0 1 X Y Z W !X !Y

5. What kind of gate is this if 0 = TRUE and 1 = FALSE? X Y !X !Y W Z 0 0 1 1 0 1 X Y Z 0 = TRUE = T X Y Z = X Y Z W !X !Y

6. Generalized De Morgan’s Theorem NOT all variables Change & to # and # to & NOT the result -------------------------------------------- F = X & Y # X & Z # Y & Z F = !((!X # !Y) & (!X # !Z) & (!Y # !Z)) F = !(!(X & Y) & !(X & Z) & !(Y & Z))

8. NAND Gate

9. X Y X Z Y Z F F = X & Y # X & Z # Y & Z

10. F = !(!(X & Y) & !(X & Z) & !(Y & Z)) NAND Gate