programmable logic controllers. chapter 4 part 1 fundamentals of logic
TRANSCRIPT
Programmable Logic Controllers
Chapter 4 Part 1
Fundamentalsof Logic
The Binary Concept
Many things can be thought of as existing in one oftwo states.
These two states can be defined as “high” or “low”,“on” or “off”, “yes” or “no”, and “1” or “0”.
5V
high, on, yes, 1
low, off, no, 0
BinarySignal
The Binary Concept
This two-state binary concept, applied to gates, can be the basis for making decisions.
The gate is a device that hasone or more inputs with whichit will perform a logical decisionand produce a result at itsone output.
Gate Decision Making
ANDGate
Light Switch
High Beam Switch
High Beam Light
The automotive high beam lightcan only be turned on when thelight switch AND high beam switchare on.
The Logical AND
Gate Decision Making
ORGate
Passenger Door Switch
Driver Door Switch
DomeLight
The automotive dome light willbe turned on when the passengerdoor switch OR the driver doorswitch is activated.
The Logical OR
AND Function
The outcome or output is called Y and the input signals are called A, B, C, etc.
Binary 1 represents the presence of a signal or the occurrence of some event, while binary 0 representsthe absence of the signal or nonoccurrence of the event.
AND Gate Function Application – Example 1
If all inputs are 1,the output will be 1
If any input is 0,the output will be 0
Basic Rules
The device has twoor more inputs andone output
AND Gate Function Application – Example 2
The AND gate operates like a series circuit.The light will be “on”only when bothswitch A and switch Bare closed.
OR Function
An OR gate can have any number of inputs but onlyone output.
The OR gate output is 1 if one or more inputs are 1.
OR Gate Function Application – Example 1
If one or more inputs are 1, the output will be 1
Basic Rules
If all inputs are 0,the output will be 0
OR Gate Function Application – Example 2
The OR gate operates like a parallel circuit.The light will be “on”if switch A or switch Bis closed.
NOT Function
The NOT function has only one input and one output.
The NOT output is 1 if the input is 0.The NOT output is 0 if the input is 1.
Since the output is always the reverse of the inputit is called an inverter.
NOT Gate Application – Example 1
The light will be “on” if the pushbutton is not pressed.
Acts like a normallyclosed pushbuttonin series with the output.
The light will be “off” if the pushbutton is n pressed.
NOT Gate Application – Example 2
If the power is “on” (1) and the pressure switch is not closed (0), the warningindicator will be “on”
Low-pressureindicating circuit
When the pressurerises to close thepressure switch, thewarning indicatorwill be switched "off"
NAND Function
The NAND gate functions like an AND gate with aninverter connected to its output.
The only time the NAND gate output is 0 is when all inputs are binary 1.
NOR Function
The NOR gate functions like an OR gate with aninverter connected to its output.
The only time the NAND gate output is 1 is when all inputs are binary 0.
XOR (exclusive-OR) Function
The output of this gate is HIGH only when one input or the other is HIGH, but not both.
The XOR function hastwo inputs and one output.
It is commonly used for comparison of two binary numbers.
1. The two binary states can be defined as:(a) “high” or “low”(b) “on” or “off”(c) 1” or “0”(d) all of these
2. A gate can have one or more outputs butonly one input. (True/False)
3. The ______ table shows the resulting output for each possible gate input conditions.
a. input status c. data
b. output status d. truth
4. A light that is "off" or a switch that is "open" would normally be represented by a binary 1.(True/False)
5. The OR function, implemented using contacts,requires contacts connected in series. (True/False)
6. With an AND gate, if any input is 0, the output will be 0. (True/False)
7. The symbol shown is that of a(an)
_________ .
(a) AND gate(b) OR gate(c) NAND gate(d) inverter
9. The basic rule for an XOR function is that ifone or the other, but not both, inputs are 1 theoutput is 1. (True/False)
10. A NAND gate is an AND gate with an inverterconnected to the output. (True/False)
8. Which of the following gates is commonly used
for the comparison of two binary numbers?(a) NAND(b) NOR(c) XOR(d) NOT
Gate Boolean Equations
AB
YAND Y = A B
Gate Boolean Equation
ORA
BY Y = A + B
NOTA Y Y = A
Boolean Equation – Example 1
Each logic function can be expressed in terms of aBoolean expression
Boolean Equation – Example 2
Any combination of control can be expressed in terms of a Boolean equation
ABY = AB + C
A + B
Y = (A + B) C
Boolean Equation – Example 2
AB
Y = AB + C
A + BY = (A + B) C
Circuit Development Using A Boolean Expression – Example 1
Circuit Development Using A Boolean Expression – Example 2
Producing A Boolean Expression From A GivenCircuit – Example 1
Producing A Boolean Expression From A GivenCircuit – Example 2