Chapter 3 Basic Logic Gates 1 Objectives n

Chapter 3 Basic Logic Gates 1

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

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

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

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

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

The AND Gate 6

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

The OR Gate n 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 n If A = 0 and B = 0, then X = 0 n 8

The OR Gate 9

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

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

Timing Analysis 12

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

n Enable and Disable Functions Enable function using AND gate 14

n Enable and Disable Functions Disable function using OR gate 15

Using Integrated Circuit Logic Gates Enable and Disable n Pin Connections n 16

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

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

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

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

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

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

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

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

Logic Gate Waveform Generation Repetitive waveform n Waveform generator n n Johnson shift counter 25

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

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

Using IC Logic Gates n Hex - six gates 28

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

Common IC Logic Gates 30

IEEE/IEC Standard Logic Symbols 31

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

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

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

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

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

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

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. n There are several integrated circuits available in both TTL and CMOS that provide the basic logic functions. n 38

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. n An inverter provides an output that is the complement of its input. n 39

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

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