Digital Fundamentals

1. Digital Fundamentals LOGIC GATES

2. The Inverter • Inverter (NOT circuit) performs the operation called inversion or complementation. • Changes 1 to 0 and 0 to 1. • Standard logic symbols. Distinctive shape symbol with negation indicators. Rectangular outline symbol with polarity indicator.

3. The Inverter – Truth Table

4. The Inverter – Operation • When the input is LOW, the output is HIGH. • When the input is HIGH, the output is LOW.

5. The Inverter – Logic Expression • X = A • If A = 0, X = 1 • If A = 1, X = 0

6. The Inverter – Application Example • Producing 1’s complement of an 8 – bit binary number.

7. AND Gate • Gate is used to describe a circuit that performs a basic logic operation. • AND gate is composed of two or more inputs and a single output.

8. AND Gate - Operation • For a 2 – input AND gate, output X is HIGH if input A and input B is HIGH, X is LOW if either A or B is LOW, or if both A and B are LOW.

9. AND Gate – Truth Table Total number of possible combinations of binary inputs to gate: N = 2n

10. AND Gate – Pulsed Operation

11. AND Gate – Logic Expression X = AB

12. AND Gate – Application Example Seat Belt Alarm System

13. OR Gate • Can have two or more inputs

14. OR Gate - Operation • For a 2 – input OR gate, output X is HIGH if either input A or input B is HIGH, or if both A and B are HIGH; X is LOW if both A and B are LOW.

15. OR Gate – Truth Table

16. OR Gate – Pulsed Operation

17. OR Gate – Logic Expression

18. OR Gate – Application Example Intrusion detection system

19. NAND Gate • Can be used as a universal gate; NAND gates can be used in combination to perform the AND, OR, and inverter operations. • NAND – contraction of NOT – AND and implies an AND function with a inverted (complement) output.

20. NAND Gate - Operation • For a 2 – input NAND gate, output X is LOW if inputs A and B are HIGH; X is HIGH if either A or B is LOW, or if both A and B are LOW.

21. NAND Gate – Truth Table

22. NAND Gate – Pulsed Operation

23. NAND Gate – Equivalent Operation Negative – OR • For a 2 – input NAND gate, performing a negative – OR operation, output X is HIGH if either input A or input B is LOW, or if both A and B are LOW.

24. NAND Gate – Logic Expression

25. NOR Gate • Can be used as universal gate; can be used in combination to perform the AND, OR, and inverter operations. • Term NOR is a contraction of NOT – OR and implies an OR function with an inverted (complement) output.

26. NOR Gate - Operation • For a 2 – input NOR gate, output X is LOW if either input A or input B is HIGH, or if both A and B are HIGH; X is HIGH if both A and B are LOW.

27. NOR Gate – Truth Table

28. NOR Gate – Pulsed Operation

29. NOR Gate – Equivalent Operation Negative – AND • For a 2 – input NOR gate, performing a negative – AND operation, output X is HIGH if both input A and B is LOW.

30. NOR Gate – Logic Expression

31. Exclusive - OR • XOR for short

32. Exclusive – OR - Operation • For an exclusive – OR gate, output X is HIGH if input A is LOW and input B is HIGH, or if input A is HIGH and input B is LOW; X is LOW if A and B are both HIGH or both LOW.

33. Exclusive – OR – Truth Table

34. Exclusive – OR – Pulsed Operation

35. Exclusive - NOR • XNOR for short.

36. Exclusive – NOR - Operation • For an exclusive – NOR gate, output X is LOW and input B is HIGH, or if A is HIGH and B is LOW; X is LOW if A and B are both HIGH or both LOW.

37. Exclusive – NOR – Truth Table