1. Chapter 3
Basic Logic Gates 1

2. Objectives You should be able to:
Describe the operation and use of AND gates and OR gates.
Construct truth tables for AND and OR gates.
Draw timing diagrams for AND and OR gates.
Use timing analysis to describe the operation of an ENABLE function. 2

3. Objectives (Continued)
Sketch external connections to IC chips to implement AND and OR logic circuits.
Explain how to use a logic pulser and a logic probe to troubleshoot digital ICs.
Describe the operation and use of NAND and NOR gates.
Construct truth tables for NAND and NOR gates. 3

4. Objectives (Continued) Draw timing diagrams for NAND and NOR gates.
Use the outputs of a Johnson shift counter to generate specialized waveforms using combinations of the five basic gates.
Develop a comparison of Boolean equations and truth tables for the five basic gates. 4

5. Logic Gates are the building blocks of Digital Electronic Circuits
Logic Gates have one Output Terminal and one or more Input Terminals
The Output will be High (1) or Low (0), depending on the value of the Inputs and the type of Gate

6. The AND Gate
The output, X, is HIGH if input A AND input B are both HIGH.
If A = 1 and B = 1, then X = 1.
If A = 0 or B = 0, then X = 0. 5

7. The AND Gate 6

8. The AND Gate Boolean Equation: X = A•B or X = AB
Read as “X equals A AND B”
Can have more than two inputs
Number of input/output combinations = 2N
N = number of input bits 7

9. The OR Gate
The output at X will be HIGH whenever input A OR input B is HIGH or both are HIGH
If A = 1 and/or B = 1, then X = 1
If A = 0 and B = 0, then X = 0 8

10. The OR Gate 9

11. The OR Gate Boolean Equation: X = A + B Can have more than two inputs
Read as, “ X = A or B”
Can have more than two inputs
Number of combinations = 2N
N = number of input bits 10

12. Timing Analysis
Timing diagrams are used to analyze the output response to varying inputs
Oscilloscope
Display plots voltage versus time
Dual-trace can display two waveforms at a time.
Logic analyzer
Can display state tables that show binary levels on signal lines
Can display up to 16 waveforms at a time 11

13. Timing Analysis 12

14. Timing Analysis
Determine the gate output for the input waveforms below. 13

15. Enable and Disable Functions
Enable function using AND gate 14

16. Enable and Disable Functions
Disable function using OR gate 15

17. Using Integrated Circuit Logic Gates
Enable and Disable
Pin Connections 16

18. Introduction to Troubleshooting Techniques
The procedure used to find the fault or trouble in a circuit.
Logic Probe shows voltage level
Indicator lamp glows strongly if high
Lamp is off if output is low
Glows dimly if floating
Floating - open circuit, neither high nor low
Logic Pulser – provides a known digital signal to a circuit 17

19. Discussion Points
Describe how a logic probe and pulser could be used to troubleshoot an AND gate.
Describe how a logic probe and pulser could be used to troubleshoot an OR gate. 18

20. The Inverter Used to complement (invert) a digital signal
When A = 1, X = 0
When A = 0, X = 1 19

21. The Inverter Truth Table Boolean Equation: X = A Inversion bar
NOT gate 20

22. The NAND Gate Same as the AND gate except that its output is inverted
If A = 1 and B = 1, X = 0
If A = 0 or B = 0, A = 1 21

23. The NAND Gate Truth Table Boolean Equation: X = AB
Multiple inputs - the output is always HIGH unless all inputs go HIGH 22

24. The NOR Gate Same as the OR gate except that its output is inverted
If A = 1 or B = 1, X = 0
If A = 0 and B = 0, X = 1 23

25. The NOR Gate
Truth Table
Boolean Equation: X = A + B 24

26. Logic Gate Waveform Generation
Repetitive waveform
Waveform generator
Johnson shift counter 25

27. Discussion Point
Which Johnson counter outputs must be connected to a 3-input AND gate to enable only CP #4? 26

28. Discussion Point
Sketch the output waveform resulting from inputting the Johnson counter outputs shown: 27

29. Using IC Logic Gates
Hex - six gates 28

30. Using IC Logic Gates Quad - four gates
Three-, four-, and eight-input configurations 29

31. Common IC Logic Gates 30

32. IEEE/IEC Standard Logic Symbols31

33. Discussion Point
Briefly describe the operation of each of the basic logic gates:
AND OR
NOT (inverter)
NAND
NOR 32

34. Discussion Point Create a truth table for a three input NAND gate.
Write the Boolean equation for a 3 input OR gate. 33

35. Discussion Point
Sketch the output waveform (X) for the 2-input AND gate shown. 34

36. Discussion Point
Sketch the output waveforms for the Johnson shift counter outputs shown: 35

37. Discussion Point
Determine the problem (if any) with the 7427 NOR IC using the logic probe results shown: 36

38. Summary
The AND gate requires that all inputs are HIGH in order to get a HIGH output.
The OR gate outputs a HIGH if any of its inputs are HIGH.
An effective way to measure the precise timing relationships of digital waveforms is with an oscilloscope or a logic analyzer. 37

39. Summary
Beside providing the basic logic functions, AND and OR gates can also be used to enable or disable a signal to pass from one point to another.
There are several integrated circuits available in both TTL and CMOS that provide the basic logic functions. 38

40. Summary
Two important troubleshooting tools are the logic pulser and the logic probe. The pulser is used to inject pulses into a circuit under test. The probe reads the level at a point in a circuit to determine is it is HIGH, LOW, or floating.
An inverter provides an output that is the complement of its input. 39

41. Summary A NAND gate outputs a LOW when all of its inputs are HIGH.
A NOR gate outputs a HIGH when all of its inputs are LOW.
Specialized waveforms can be created by using a repetitive waveform generator and the basic gates. 40

42. Summary
Manufacturers’ data manuals are used by the technician to find the pin configuration and operating characteristics for the ICs used in modern circuitry. 41