1. Introduction to Computer Engineering by Richard E. Haskell Basic Logic Gates Module M1.1 Section 3.1

2. Introduction to Computer Engineering by Richard E. Haskell Basic Logic Gates NOT, AND, and OR Gates NAND and NOR Gates DeMorgan’s Theorem Exclusive-OR (XOR) Gate

3. Introduction to Computer Engineering by Richard E. Haskell XY Y= !X NOT NOT Gate -- Inverter X Y 0101 1010

4. Introduction to Computer Engineering by Richard E. Haskell NOT Y = !X Y = X’ Y = X Y =  X

5. Introduction to Computer Engineering by Richard E. Haskell NOT X!X!!X = X X !X !!X 0 1 0 1 0 1

6. Introduction to Computer Engineering by Richard E. Haskell AND Gate AND X Y Z Z = X & Y X Y Z 0 0 0 0 1 0 1 0 0 1 1 1

7. Introduction to Computer Engineering by Richard E. Haskell AND X & Y X Y X * Y XY U V

8. Introduction to Computer Engineering by Richard E. Haskell OR Gate OR X Y Z Z = X # Y X Y Z 0 0 0 0 1 1 1 0 1 1 1 1

9. Introduction to Computer Engineering by Richard E. Haskell OR X # Y X + Y X V Y X U Y

10. Introduction to Computer Engineering by Richard E. Haskell NAND Gate NAND X Y Z Z = !(X & Y) X Y Z 0 0 1 0 1 1 1 0 1 1 1 0

11. Introduction to Computer Engineering by Richard E. Haskell NAND Gate NOT-AND X Y Z W = X & Y Z = !W = !(X & Y) X Y W Z 0 0 0 1 0 1 1 0 0 1 1 1 1 0 W

12. Introduction to Computer Engineering by Richard E. Haskell NOR Gate NOR X Y Z Z = !(X # Y) X Y Z 0 0 1 0 1 0 1 0 0 1 1 0

13. Introduction to Computer Engineering by Richard E. Haskell NOR Gate NOT-OR X Y W = X # Y Z = !W = !(X # Y) X Y W Z 0 0 0 1 0 1 1 0 1 0 1 1 1 0 Z W

14. Introduction to Computer Engineering by Richard E. Haskell NAND Gate X Y X Y Z Z Z = !(X & Y)Z = !X # !Y = X Y W Z 0 0 0 1 0 1 1 0 0 1 1 1 1 0 X Y !X !Y Z 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0

15. Introduction to Computer Engineering by Richard E. Haskell De Morgan’s Theorem-1 !(X & Y) = !X # !Y NOT all variables Change & to # and # to & NOT the result

16. Introduction to Computer Engineering by Richard E. Haskell NOR Gate X Y Z Z = !(X # Y) X Y Z 0 0 1 0 1 0 1 0 0 1 1 0 X Y Z Z = !X & !Y X Y !X !Y Z 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0

17. Introduction to Computer Engineering by Richard E. Haskell De Morgan’s Theorem-2 !(X # Y) = !X & !Y NOT all variables Change & to # and # to & NOT the result

18. Introduction to Computer Engineering by Richard E. Haskell De Morgan’s Theorem NOT all variables Change & to # and # to & NOT the result -------------------------------------------- !X # !Y = !(!!X & !!Y) = !(X & Y) !(X & Y) = !!(!X # !Y) = !X # !Y !X & !Y = !(!!X # !!Y) = !(X # Y) !(X # Y) = !!(!X & !Y) = !X & !Y

19. Introduction to Computer Engineering by Richard E. Haskell Exclusive-OR Gate X Y Z XOR X Y Z Z = X $ Y 0 0 0 0 1 1 1 0 1 1 1 0

20. Introduction to Computer Engineering by Richard E. Haskell Exclusive-OR Gate 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 X Y !X !Y !X&Y X&!Y Z

21. Introduction to Computer Engineering by Richard E. Haskell Problem Z Write the logic equation for Z in terms of X and Y