Chapter 3 Basic Logic Gates 1

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

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

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

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

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

The AND Gate 6

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

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

The OR Gate 9

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

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

Timing Analysis 12

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

Enable and Disable Functions Enable function using AND gate 14

Enable and Disable Functions Disable function using OR gate 15

Using Integrated Circuit Logic Gates Enable and Disable Pin Connections 16

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

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

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

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

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

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

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

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

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

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

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

Using IC Logic Gates Hex - six gates 28

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

Common IC Logic Gates 30

IEEE/IEC Standard Logic Symbols 31

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

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

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

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

Discussion Point 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. 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

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

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

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

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