1. Basic Digital Logic Basic Gates

2. Digital Signals Digital Signals have two basic states:
1 (logic “high”, or H, or “on”)
0 (logic “low”, or L, or “off”)
Digital values are in a binary format. Binary means 2 states.
A good example of binary is a light (only on or off)

3. Digital Logic Hardware consists of a few simple building blocks
These are called logic gates
AND, OR, NOT, …
NAND, NOR, XOR, …
Logic gates are built using transistors
NOT gate can be implemented by a single transistor
AND gate requires 3 transistors
Transistors are the fundamental devices
Pentium consists of 3 million transistors
Compaq Alpha consists of 9 million transistors
Now we can build chips with more than 100 million transistors
Functionality can be expressed by a truth table
A truth table lists output for each possible input combination

4. Basic Gates
Basic Digital logic is based on 3 primary functions (the basic gates):
NOT Gate
AND Gate
OR Gate
Other gates
XOR Gate
NAND Gate
NOR Gate
XNOR Gate

5. The AND function Usually represented by dot (.) Ex: x.y Logics:
If all the inputs are high is the output is high
If any input is low, the output is low

6. AND Logic Symbol Output Inputs If both inputs are 1, the output is 1
If any input is 0, the output is 0

7. AND Logic Symbol
Inputs
Output
Determine the output

8. AND Logic Symbol
Inputs
Output 1
Determine the output

9. AND Logic Symbol 1 1
Inputs
Output 1
Determine the output

10. AND Truth Table
To help understand the function of a digital device, a Truth Table is used:
Input
Output 1
Every possible input combination
Truth Table for 3
inputs
AND Gate

11. AND Gates
It is possible to have AND gates with more than 2 inputs. The same logic rules apply – “if any input…”

12. AND Different Symbols X & Y X and Y X Y X * Y XY (textbook) and(Z,X,Y)V U

13. The OR Gate Usually represented by dot (+) Ex: x+y The OR function:
if any input is high, the output is high
if all inputs are low, the output is low

14. OR Logic Symbol Output Inputs If any input is 1, the output is 1
If all inputs are 0, the output is 0

15. OR Logic Symbol
Inputs
Output
Determine the output

16. OR Logic Symbol 1
Inputs
Output 1
Determine the output

17. OR Logic Symbol 1 1
Inputs
Output 1
Determine the output

18. OR Truth Table Truth Table Input Output 1 Truth Table for 3 inputs1
Truth Table for 3
inputs
OR Gate

19. NOT
Y = ~X
Y = !X
Y = not X
Y = X’
Y = X
Y = X (textook)
not(Y,X)

20. The NOT function The NOT function:
If any input is high, the output is low
If any input is low, the output is high
“The output is the opposite state of the input”
The NOT function is often called INVERTER

21. NOT Logic Symbol Input Output If the input is 1, the output is 0

22. NOT Logic Symbol
Output
Input 1
Determine the output

23. NOT Logic Symbol 1
Output
Input
Determine the output

24. NOT Truth Table
Truth Table
Input
Output 1
NOT Function

25. Exercise 1 1. Least Challenging Complete the sentences:
If all inputs of an OR gate are low, the output is_________
If any input of an AND gate is low, the output is _________
The output of a NOT gate is always the ___________ of the input.

26. Chips

27. The XOR [Exclusive OR] function
Usually represented by 
Ex: x  y
Logics:
If all inputs are high or low then the output will be low Y X + = Å

28. XOR Logic Symbol X Z
Output
Inputs Y B A + = Å

29. XOR Logic Symbol
Inputs
Output
Determine the output

30. XOR Logic Symbol 1
Inputs
Output 1
Determine the output

31. XOR Logic Symbol 1 1
Inputs
Output
Determine the output

32. XOR Logic Symbol 1
Inputs
Output 1
Determine the output

33. XOR Truth Table
Truth Table for 3
inputs
XOR Gate

34. The XNOR [Exclusive NOR] function
Usually represented by
Ex: X Y or (x  y)′
Logics:
If all inputs are high or low then the output will be high

35. XNOR Logic Symbol X Z
Output
Inputs Y
X Y =XY+X′Y′

36. XNOR Logic Symbol 1
Inputs
Output
Determine the output

37. XNOR Logic Symbol
Inputs
Output 1
Determine the output

38. XNOR Logic Symbol 1
Inputs
Output
Determine the output

39. XNOR Logic Symbol 1 1
Inputs
Output 1
Determine the output

40. XNOR Truth Table
Truth Table for 3
inputs
XNOR Gate

41. The NAND [NOT-AND] function
Usually represented by ′ or ‾
Ex: (XY)′
Logics:
If all inputs are high output will be low

42. NAND Logic Symbol
Output
Inputs

43. NAND Logic Symbol 1
Inputs
Output
Determine the output

44. NAND Logic Symbol 1
Inputs
Output 1
Determine the output

45. NAND Logic Symbol 1 1
Inputs
Output
Determine the output

46. NAND Logic Symbol 1
Inputs
Output 1
Determine the output

47. NAND Truth Table
Truth Table for 3
inputs
NAND Gate

48. The NOR [NOT-OR] function
Usually represented by ′ or ‾
Ex: (X+Y)′
Logics:
If all inputs are low output will be high

49. NOR Logic Symbol
Inputs
Output

50. NOR Logic Symbol 1
Inputs
Output
Determine the output

51. NOR Logic Symbol
Inputs
Output 1
Determine the output

52. NOR Logic Symbol 1
Inputs
Output
Determine the output

53. NOR Logic Symbol 1
Inputs
Output 1
Determine the output

54. NOR Truth Table
NOR Gate
Truth Table for 3
inputs

58. Draw a circuit diagram for  = (xy' + x'y)z.

61. (A.B+C′)D