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Chapter 3 Basic Logic Gates 1

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Objectives You should be able to: 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 operation of an ENABLE function. 2

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Objectives You should be able to: You should be able to: –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

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Objectives You should be able to: You should be able to: –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

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The AND Gate The output, X, is HIGH if input A AND input B are both HIGH The output, X, is HIGH if input A AND input B are both HIGH Figure 3-1 Figure 3-1 5

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The AND Gate Truth Table – Truth Table – 6

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The AND Gate Boolean Equation X = A AND B or X = AB Boolean Equation X = A AND B or X = AB Can have more than two inputs Can have more than two inputs Number of combinations = 2 N Number of combinations = 2 N 7

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The OR Gate The output at X will be HIGH whenever input A OR input B is HIGH or both are HIGH The output at X will be HIGH whenever input A OR input B is HIGH or both are HIGH Figure 3-5 Figure 3-5 8

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The OR Gate Truth Table - Truth Table - 9

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The OR Gate Boolean Equation X = A OR B or X = A+B Boolean Equation X = A OR B or X = A+B Can have more than two inputs Can have more than two inputs Number of combinations = 2 N Number of combinations = 2 N 10

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Timing Analysis Timing diagram Timing diagram Oscilloscope Oscilloscope –Voltage versus time –Up to two Logic analyzer Logic analyzer –State table –Up to 16 11

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Timing Analysis MultiSIM AND gate simulation. MultiSIM AND gate simulation. 12

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Timing Analysis Example of timing analysis – Example of timing analysis – –Determine the output. 13

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Enable and Disable Functions Enable function using AND gate Enable function using AND gate Figure 3-17 14

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Enable and Disable Functions Disable function using OR gate Disable function using OR gate Figure 3-18 15

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Using Integrated Circuit Logic Gates Enable and Disable Enable and Disable Pin Connections Pin Connections V CC and GND V CC and GND Figure 3-20 16

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Introduction to Troubleshooting Techniques The procedure used to find the fault or trouble in a circuit. The procedure used to find the fault or trouble in a circuit. Logic Probe Logic Probe –Metal tip –Indicator lamp(s) Floating - open circuit, neither HIGH nor LOW Floating - open circuit, neither HIGH nor LOW Logic Pulser - provide known digital signal to a circuit Logic Pulser - provide known digital signal to a circuit 17

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

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The Inverter Used to complement or invert a digital signal Used to complement or invert a digital signal Figure 3-27 Figure 3-27 19

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

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The NAND Gate Same as the AND gate except that its output is inverted Same as the AND gate except that its output is inverted Figure 3-29 Figure 3-29 21

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

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The NOR Gate Same as the OR gate except that its output is inverted Same as the OR gate except that its output is inverted Figure 3-36 Figure 3-36 23

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The NOR Gate Truth Table Truth Table Boolean Equation X = A + B Boolean Equation X = A + B See Table 3-8 in your text 24

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Logic Gate Waveform Generation Repetitive waveform Repetitive waveform Waveform generator Waveform generator –Johnson shift counter –Figure 3-43 25

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

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

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Using IC Logic Gates Hex - six gates Hex - six gates Figure 3-60 Figure 3-60 28

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Using IC Logic Gates Quad - four gates Quad - four gates three-, four-, and eight-input configurations three-, four-, and eight-input configurations Figure 3-61 Figure 3-61 29

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Summary of Basic Logic Gates and IEEE/IEC Standard Logic Symbols 30

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Summary of Basic Logic Gates and IEEE/IEC Standard Logic Symbols Figure 3-65 31

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

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

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

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

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

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

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

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

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Summary A NAND gate outputs a LOW when all of its inputs are HIGH 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 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 Specialized waveforms can be created by using a repetitive waveform generator and the basic gates 40

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

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