1. Instructor: Alexander Stoytchev
CprE 281: Digital Logic
Instructor: Alexander Stoytchev

2. NAND and NOR Logic Networks
CprE 281: Digital Logic
Iowa State University, Ames, IA
Copyright © Alexander Stoytchev

3. Administrative Stuff
HW2 is due today

4. Administrative Stuff HW3 is out It is due on Monday Sep 15 @ 4pm.
Please write clearly on the first page (in BLOCK CAPITAL letters) the following three things:
Your First and Last Name
Your Student ID Number
Your Lab Section Letter
Also, please
Staple your pages
Use Letter-sized sheets

5. Quick Review

6. The Three Basic Logic Gatesx 1 2 × x 1 2 + x
NOT gate
AND gate
OR gate
[ Figure 2.8 from the textbook ]

7. Truth Table for NOT x 1 x

8. Truth Table for AND x 1 2 ×

9. Truth Table for OR x 1 2 +

10. DeMorgan’s Theorem

11. Example 2.10
Implement the function f(x1, x2, x3) = Σ m(2, 3, 4, 6, 7)

12. Minterms and Maxterms (with three variables)
[ Figure 2.22 from the textbook ]

13. Minterms and Maxterms (with three variables)

14. The SOP expression is:
This could be simplified as follows:

15. Example 2.12 Implement the function f(x1, x2, x3) = Π M(0, 1, 5),
which is equivalent to f(x1, x2, x3) = Σ m(2, 3, 4, 6, 7)

16. Minterms and Maxterms (with three variables)

17. The SOP expression is:
This could be simplified as follows:

18. Two New Logic Gates

19. NAND Gate x1 x2 f 1

20. NOR Gate x1 x2 f 1

21. AND vs NAND x 1 2 × x 1 2 × x1 x2 f 1 x1 x2 f 1

22. AND followed by NOT = NANDx 1 2 × x 1 2 × x1 x2 f 1 f 1 x1 x2 f 1

23. NAND followed by NOT = ANDx 1 2 × x 1 2 × x 1 2 × x 1 x 2 x1 x2 f 1 f 1 x1 x2 f 1

24. OR vs NOR x 1 2 + x1 x2 f 1 x1 x2 f 1

25. OR followed by NOT = NOR x 1 2 + x1 x2 f 1 f 1 x1 x2 f 1

26. NOR followed by NOT = OR x 1 2 + x 1 2 + x1 x2 f 1 f 1 x1 x2 f 1

27. Why do we need two more gates?

28. Why do we need two more gates?
They can be implemented with fewer transistors.
(more about this later)

29. They are simpler to implement, but are they also useful?

30. Building a NOT Gate with NANDx x x f 1 x 1

31. Building a NOT Gate with NANDx x x f 1 x 1
impossible
combinations

32. Building a NOT Gate with NANDx x x f 1 x 1
impossible
combinations
Thus, the two truth tables are equal!

33. Building an AND gate with NAND gates[

34. Building an OR gate with NAND gates[

35. Any Boolean function can be implemented
Implications
Any Boolean function can be implemented
with only NAND gates!

36. NOR gate with NAND gates[

37. XOR gate with NAND gates[

38. XNOR gate with NAND gates[

40. Building a NOT Gate with NORx x x x f 1 x 1

41. Building a NOT Gate with NORx x x x f 1 x 1
impossible
combinations

42. Building a NOT Gate with NORx x x x f 1 x 1
impossible
combinations
Thus, the two truth tables are equal!

43. Building an OR gate with NOR gates[

44. Let’s build an AND gate with NOR gates

45. Any Boolean function can be implemented
Implications
Any Boolean function can be implemented
with only NOR gates!

46. NAND gate with NOR gates[

47. XOR gate with NOR gates [

48. XNOR gate with NOR gates[

49. The following examples came from this book

50. [ Platt 2009 ]

51. [ Platt 2009 ]

52. [ Platt 2009 ]

53. DeMorgan’s theorem in terms of logic gatesx 1 x 1 2 x 1 x x 2 2
(a) x x = x + x 1 2 1 2

54. DeMorgan’s theorem in terms of logic gatesx 1 x x 1 1 x x 2 x 2 2
(b) x + x = x x 1 2 1 2

55. Function Synthesis

56. Using NAND gates to implement a sum-of-productsx 1 2 3 4 5
[ Figure 2.27 from the textbook ]

57. Using NOR gates to implement a product-of sumsx 1 2 3 4 5
[ Figure 2.28 from the textbook ]

58. Example 2.13 Implement the function f(x1, x2, x3) = Σ m(2, 3, 4, 6, 7)
using only NOR gates.

59. Example 2.13 The POS expression is: f = (x1 + x2) (x2 + x3)
Implement the function f(x1, x2, x3) = Σ m(2, 3, 4, 6, 7)
using only NOR gates.
The POS expression is: f = (x1 + x2) (x2 + x3)

60. NOR-gate realization of the functionx1 f
(a) POS implementation
(b) NOR implementation x3 x2
[ Figure 2.29 from the textbook ]

61. Example 2.14 Implement the function f(x1, x2, x3) = Σ m(2, 3, 4, 6, 7)
using only NAND gates.

62. Example 2.14 The SOP expression is: f = x2 + x1x3
Implement the function f(x1, x2, x3) = Σ m(2, 3, 4, 6, 7)
using only NAND gates.
The SOP expression is: f = x2 + x1x3

63. NAND-gate realization of the functionx1 f x2 x3
(a) SOP implementation x1 f x2 x3
(b) NAND implementation
[ Figure 2.30 from the textbook ]

64. Questions?

65. THE END