Topic Finder for Chapter 2
Introduction
Background Information
The AND Operation
The OR Operation
Technical Principles
Active Logic Signals
Active Logic
Signal Concept Process Example
Getting Started with
Digital Devices
Chapter 2 Overview
Review Questions
List of Figures
Figure 2.1 Car Safety
Ignition Sequence
Figure 2.2 Car Door
Alarm Logic
Figure 2.3 14 Pin TTL
Package
Figure 2.4 AND Arrangement
in 7408
Figure 2.5 7408 Installed
on BreadBoard
Figure 2.6 Wire Connection
to 7408
Figure 2.7 Car Ignition
Logic Table
Problem 2.11 Variety
of Button and Relay Connections
As suggested earlier, the second practical user concern with respect to logic devices is that the user's own logic thought process be sound. Human beings and machines that human beings build can make logic decisions. The big difference between the two is that the machines, as long as they are not broken, never make a mistake in the logic. The fact that machines are better logic operators than we are is the driving force to make these logic tools work faster and perform complicated logic operations. It is one of the main reasons that digital logic circuits have been perfected to their current state.
To appreciate the whole idea of digital devices as controllers of a logic process, it is useful to first review some simple logic operators and show how electric circuits can perform these simple logic operations. In your first few laboratories you will use digital logic devices to make small logic device based circuits to accomplish a few simple logical control tasks. You will also be asked to design and construct a digital device circuit to solve a more complicated process logic problem.
There are four elementary logic operations. We will focus on two of them, i.e. the AND operation and the OR operation. The two elementary logic operations we will not discuss at this time, i.e. the NAND and the NOR, are closely related to the AND and the OR operation. Perhaps you can explore the library to find more information about the NAND and the NOR operations. Any book on Digital Circuits will provide such information.
Figure 2.1 illustrates two ways to visualize the AND operation. The top portion of the figure has a graphic representation while the bottom half of the figure shows a tabular format. Some explanation of this figure may be in order. Although it may not be defined in your brain as a specific type of thought process, you are already familiar with the AND operation. Consider a common situation most of you have been involved in. You get into a car, turn the ignition key to the ON position, and forget to buckle your seat belt. All late model cars will remind you of your mistake by lighting a warning lamp on the car's dashboard. Most cars will also ring a buzzer. In fact, most cars do both. In any event, you have just been through a logic process in which the car was aware of the fact that the ignition is in the ON position AND you left the seat belt buckle in the OPEN position. As a result of these two facts the warning light and/or buzzer, was turned on.
The AND operation we are working with can be expressed in another way. If it is true that the car ignition key is in the ON position AND it is true that the seat belt buckle is in the OPEN position, then the warning light must be ON. As long as this statement is followed then whoever or whatever generates the appropriate action to insure that the warning light is ON is performing an AND operation.
Figure 2.1A shows a visual shorthand way to express this AND operation. The two input conditions are shown on the left side of the diagram. The action to be taken when both input conditions are met as stated on the right side of the drawing. The vertical almost half circle shape between the inputs and the output statement is the symbol for the AND operation. Thus when an engineer sees the words and symbols in Figure 2.1A, that engineer knows that an AND operation is involved in the process. In this case, the engineer knows that the warning light will go on only when the car ignition key is in the ON position AND the seat belt buckle is in the OPEN, i.e. not buckled, position. When an AND device, which may be anything human or otherwise, performs an AND operation correctly, it will only turn the warning light ON if these two input conditions are true.
The table shown in Figure 2.1B is an alternate way to express an AND operation. This method is not as popular with engineers because it takes more time to make. More significantly, if a situation is involved with a lot of logic operations it is easier to understand the complete logic scheme using a collection of symbols than a big logic table. (Perhaps your philosophy instructor would disagree, but philosophy professors seldom have to figure out all of the nitty gritty logic operations associated with the operation of a cracking tower, a car or a space shuttle.)
In any event, a logic table is easy to construct and when kept small, they are easy to read. The example in Figure 2.1B is for the car seat belt example we have been working with. The first column lists all the conditions for the car ignition key. The second column has the possible conditions for the seat belt buckle while the third column summarizes the results for each combination of key and buckle position. The first row of the table summarizes the situation when it is true that the ignition key is in the ON position and it is true that the seat belt buckle is in the OPEN position, (not buckled). Under these conditions, it is true that the warning light is ON. In other words if the two input conditions to this AND operations are true the output condition must be also be true.
There is an alternate way to say the same thing. If the two input condition questions are asked, "Is the car ignition key in the ON position?"; and "Is the seat belt buckle in the OPEN position?", and the answer to both of these questions is YES then the answer to the response question, "Is the warning light ON?", must be yes. It is the responsibility of any and all AND devices to make sure that if the answer to all of the input questions is YES, that the answer to the output question is YES. If the AND device does not do this every time it checks the status of the input questions, then it is broken or faulty and must be replaced. In addition to the idea of the logic device being broken, the number of times it checks the status of its inputs is important. Digital logic devices, such as the ones you will be using in the laboratory check their input signals every microsecond. Similar mechanical devices may check their input signals every millisecond, while humans may check their input signals once or twice before being distracted or bored. Thus even if the logic device does its work correctly, that is of minimal significance in a control situation if it does not check the status of its inputs frequently enough. To be useful a logic device must check its input conditions at least twice as fast as the fastest input to that device can respond to the process to be controlled.
The automobile also has OR devices in it. One easy example of an OR operation is summarized in Figure 2.2. Figure 2.2A shows the symbol for a two input OR operation. The two input condition OR questions are "Is the driver's door OPEN?", and "Is the passenger's door OPEN?", and are shown on the left side of the diagram. The output condition OR question, "Is the warning light ON?", is provided on the right side of the drawing. The quarter moon shape between the input and output conditions is the symbol for the OR operation.
The OR operation functions just as the word OR suggests. If the driver's door is in the OPEN position OR if the passenger's door is in the OPEN position, then the warning light will be on. Either door can be open to produce a positive output signal. In fact the only time the warning lamp will not be light is when both doors are closed, or not in the OPEN position.
The OR table summarizes the same information. Notice that the only time the answer to the question "Is the warning light ON?" is "No", is when the answer to the questions about the driver's and passenger's doors, is no. Therefore, the two input OR device that monitors the car's driver and passenger door is only operating correctly when it keeps the warning light on if either or both doors are open. If it does not do this correctly all of the time, it is broken or faulty and must be replaced.
You should now understand why man-made logic devices perform logic operations better than humans do. As long as a non-human logic device is not broken, it always works and always works correctly. Humans that are not broken don't always work, they sleep sometimes, they get tired sometimes and they certainly get bored sometimes. All of this assures that even when they are working they often make simple logic mistakes.
Over the years AND and OR devices have been made in a variety of ways, the integrated circuit, i.e. the IC, is one of the newest and best efforts. It has been applied to many applications in our modern society. These are the logic devices that we will investigate in many of the experiments in this laboratory based course. An integrated circuit is a combination, an integration, of small transistors and other circuit component such as resistors stuffed into a plastic package. This package is electrically designed to perform a specific task.
Figure 2.3 shows an illustration of a IC package. The actual integrated circuits are inside the package and the wires, i.e. the leads, that come out of the package are used to make the electrical connections to the various parts of the tiny circuits hidden inside the plastic case. The number 7408 stamped on the top of the package represents one of the many identification numbers that might be put on the package. The number 7408 indicates that the package has AND devices in it. If the number were 7432, then the package would have OR devices in it. There is a different number for each type of circuit package. The package also has a code number that identifies where the package was made.
Figure 2.4 provides an artist's view of the inside of an AND package. Although the inside of the package is much more complicated than suggested, the drawing does show how the AND devices are arranged in the package. There are four AND devices in the 7408 package. The first one uses pins 1, 2 and 3. Pin 1 and Pin 2 are the two input pins while Pin 3 is the output pin. The other three device pin connections are clearly shown. You should agree that pin 6, pin 8 and pin 11 are the output pins for each of the three other AND devices in the package. In this diagram, pin 14 is used to make the high voltage connection to the devices while pin 7 is used for the low voltage connection. For the 7408 and the 7432, pin 14 is connected to 5 volts while pin 7 is connected to zero volts.
A breadboard is a convenient way to make electrical connections to IC packages, or chips, and various other electrical devices. Figure 2.5 shows a 7408 IC package set in a breadboard. The package is placed such that it straddles the depression in the center of the breadboard. Connections can now be made to the different pins of the package by putting wires in any of the holes in the row containing the pin that we wish to connect. This allows us to use the IC chips many times without making direct connections to the pins, which are very fragile. Care must still be taken when putting the IC packages into the breadboard. It really is easy to bend or destroy the pin connections to the package.
Figure 2.6 show the cut away view of the 7408 with suggested wire connections for the AND logic task summarized in Figure 2.1. The device will make the correct logic decision provided the connections to the device are correct. For our automobile example, the engineer has to match the switch circuit wire from the ignition key circuit and the wire from the seat belt circuit with the desired input pins of the AND device. The output pin from the AND device has to be connected to the dashboard warning light circuit so that it can light the warning light when the AND input conditions are met.
Figure 2.7 illustrates the idea of using a voltage to determine the logic state. Although it is convenient for humans to perform logic operations by using questions that can be answered with a "yes" or a "no", that is not a useful way for an electronic AND device to do logic. Integrated circuit logic devices are designed to respond to two different voltage levels. For the devices we will use, the AND responds to 5 volts (YES), and to zero volts (NO), signals delivered to its input pins to provide either a 5 volts or zero volts output signal to the warning light circuit. The warning lamp will light if 5 volts is supplied to the AND's output pin. The lamp will go off if zero volts is supplied to the lamp.
The top portion of Figure 2.7 shows all of the possible ways the 5 volt and zero volt input signals produce an output signal. The lower section of the figure indicates that the AND logic table for the car ignition example would be the same as shown in Figure 2.1B except the YES entries would be replace with 5 volts and the NO entries would be replaced with 0 volts. It is important to remember that the an IC AND device expects that voltage signals be sent to its inputs. In return for this, the IC AND device will provide either a 5 volt or a 0 volt signal at its output pin. It is this output signal that is responsible for making the warning light go on or off for our example. It is the engineer's responsibility to make sure that the AND's output pin is connected to the correct wire in the warning light circuit.
An easy way to keep track of what the expected
results of a Logic operation is going to be is to adapt and use as often
as possible the concept of an Active Logic Signal. The quickest way
to explain this concept is to just consider a simple example. Although
this is an over simplified example it should indicate the usefulness of
this active logic signal concept.
Active
Logic Signal Concept Process Example
Suppose you wish to develop a simple control scheme that will open an auxiliary valve if the pressure of the fluid at the pump inlet is to low OR the temperature of the pump is to high. For this example story, the presumption will be that opening this auxiliary value allows more fluid to reach the inlet of the pump. This extra fluid will increase the amount of fluid (and its pressure) at the inlet of the pump and allow the pump to work more efficiently which, in turn, allows the pump to run cooler. Fortunately, you have access to instrumentation technicians who can wire the sensors and final control relay to the circuit you suggest. Thus the issue at this point is straight forward. What is the logic control circuit for this situation?
Upon review of the control conditions the answer is very easy. Two digital sensors are required. One is a Temperature Sense High, TSH, device while the other is a Pressure Sense Low, PSL. The control logic is also simple and can be easily stated in terms of this active logic signal convention.
1) When the TSH is active OR the PSL is active the valve should open.
If the active logic signal concept is expanded a little, it can include the idea of a passive logic signal. Now the control scheme above can be restated in a passive voice.
2) If the TSH AND the PSL are passive the valve should be closed.
Finally, the idea of active or passive can be assigned to the valve position as well. A choice must be made. In this case, the valve open position will be identified as the active position and the logic signal that makes the valve open is identified as the active signal. With this in mind the two logic statements can be stated again.
1) When the TSH is active OR the PSL is active the valve is active.
2) If the TSH AND the PSL are passive the valve is passive.
This idea of an active sensor or final control element is certainly new to you and will need a little time to get use to. However, it is a very useful concept that makes it much easier to develop your own or read someone else's control diagrams. Also note that the example above has two ways to describe the same situation. In the Active Logic mode, the OR word was used. The Or operation was the perfect logic thought process to describe the control conditions given the view point of the human was an action by the final control element if either of the two sensors in the situation went into alarm. In the Passive logic mode, the AND word was used. The AND operation was the perfect logic thought process to describe the control conditions given the view point of the human was no action by the final control element when both of the sensors in the situation were not in alarm.
Go back to the two statements
above that describe the control conditions and think about them until you
really understand that the two ways (the active logic mode and the passive
logic mode) of stating the situation are really absolutely equivalent.
(Don't ignore this advise and skip that exercise. The time spent
right now thinking about this method of communication will pay off big
time later in the course.)
Getting Started With Digital Devices
One of the best ways to begin to work with TTL logic devices is to memorize the pinout for one package and then experiment with that package. The 7408 is a good candidate package for this task. The graphic pinout is shown in Figure 2.5. The power connection for the package is at pin 14. The ground connection for the package is at pin 7. The four two input AND devices in the package are clearly shown. The input pins for one AND device are at pin 1 and pin 2. The output pin for that device is at pin 3. If you put pin 14 and 5 volts and pin 7 at 0 volts, (i.e. ground) the devices in the package will work independent of each other. If you put pin 1 at 5 volts, pin 2 at 5 volts and connect pin 3 to a LED, (light emitting Diode), the light will shine. Any other combinations of voltage signals ( i.e. 5 volts or 0 Volts only please) will cause the LED to go OFF. When you get into lab please try it, its fun. Then try the other devices in the package as well.
2. 1 In the space provide below on this page indicate:
a) the Truth table for an AND device?
b) the Truth table for an OR device?
c) the Truth table for a NOR device?
d) the Truth table for a NAND device?
2. 2 Draw a function diagram for a logic operation that has two independent two input OR devices attached to a single two input AND device which in turn is attached to the input of an invertor device.
2. 3 Label the OR inputs of the function diagram in question 2.2 with one of the first 4 letters of the alphabet. Label the outputs of each of the devices in diagram with one of the last 4 letters of the alphabet. Construct the Truth table for this function diagram and present it in the space below.
2. 4 Draw a function diagram for the circuit illustrated in Figure 2.6
2. 5 Consider the following control situation;
An industrial saw operates if all of the safety conditions are met and the START Push Button has been pushed and released. The saw must stop when the STOP push button is pushed. For this simplified example there is only one safety condition. The saw will not run if the safety shield is not in place. Assume that the saw runs because a 0 volt signal is supplies to one of the coil inputs on a relay. ( the other coil input is always at 5V.) The high voltage side of the relay is wired as shown in figure 1.1
a) Draw a function diagram for this control idea. Include both the low voltage coil side and high voltage load side of the relay in your function diagram. Clearly indicate how your logic operations are to be attached to the relay.
b) Draw a circuit diagram for this control idea.
2. 6 Draw a function diagram for a circuit that will decide if any of three sensor signals, i.e. a Temperature Sense Low device,(TSL), or a Pressure Sense High device, (PSH), or a Level Sense High device,(LSH), and a start signal are at 5 volts. If this condition is met the circuit will generate a 5 volt signal.
2. 7 Repeat problem 2.09 but the circuit should generate a 0 volt signal if the condition is met.
2. 8 Examine Figure 1.4 and find the package (chip) labeled NE555. Also identify the three process input signals labeled P Control, ORA Reference, and Count. What logic signal is required on each of these three control lines to put;
a logic 1 at pin 2 of the NE555 (i.e. the ON signal for this process)? ( Use an X as the signal on the control line if it does not make any difference what the logic signal on that line is.)
a logic 0 at pin 2 of the NE555?
a logic 1 at pin 4 of the NE555 (i.e. the OFF signal for this process)?
2. 9 Examine Figure 1.4 and find the output signal line that is labeled as an 11. Also identify the three process input signals labeled P Control, ORA Reference, and Count. What logic signal is required on each of these three control lines to put a logic 1 signal on the output signal line labeled as an 11?
2.10 Examine Figure 1.4 and find pin 2 of the 7404. What does the RC circuit do to the signals coming for pin 2?
2.11 Examine the set of push buttons and relays provided in the figure.
Indicate voltage at the points indicated assuming the buttons are
actually in the exact positions as shown in the diagram.
(a) (b)
(c) (d)
indicate if the motor is running or not for each of the relays indicated
below assuming the relay contacts are actually in the position as shown
in the diagram.
(e) (f)
(g) ( h)
2.12 Examine the figure for
this problem and determine?
(a) What is the logic signal ( logic 0 or logic
1) needed if there is to be a
"Stop" command
for a "Human" reason?
(b) What is the logic signal needed if there
is to be a "Stop" command
for a "Process"
reason?
(c) What is the control logic signal (logic
1 or logic 0) at the coil of the
relay
if there is no "human" or "process" Stop command from the
process?