1. Programmable Logic Controllers
Third Edition
Frank D. Petruzella
McGraw-Hill

2. Chapter 4
Fundamentals
of Logic

3. The Binary Concept Many things can be thought of as existing in one of
two 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
Binary
Signal

4. The Binary Concept
This two-state binary concept, applied to gates, can be
the basis for making decisions.
The gate is a device that has
one or more inputs with which
it will perform a logical decision
and produce a result at its
one output.

5. Gate Decision Making The Logical AND Light Switch AND High Beam Gate
High Beam Switch
The automotive high beam light
can only be turned on when the
light switch AND high beam switch
are on.

6. Gate Decision Making The Logical OR Passenger Door Switch OR Dome Gate
Light
Driver Door Switch
The automotive dome light will
be turned on when the passenger
door switch OR the driver door
switch is activated.

7. 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 represents
the absence of the signal or nonoccurrence of the event.

8. AND Gate Function Application – Example 1
Basic Rules
The device has two
or more inputs and
one output
If any input is 0,
the output will be 0
If all inputs are 1,
the output will be 1

9. AND Gate Function Application – Example 2
The AND gate operates
like a series circuit.
The light will be “on”
only when both
switch A and switch B
are closed.

10. OR Function An OR gate can have any number of inputs but only
one output.
The OR gate output is 1 if one or more inputs are 1.

11. OR Gate Function Application – Example 1
Basic Rules
If all inputs are 0,
the output will be 0
If one or more inputs are 1, the output will be 1

12. OR Gate Function Application – Example 2
The OR gate operates
like a parallel circuit.
The light will be “on”
if switch A or switch B
is closed.

13. 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 input
it is called an inverter.

14. NOT Gate Application – Example 1
Acts like a normally
closed pushbutton
in series with the
output.
The light will be “on” if the pushbutton is not pressed.
The light will be “off” if the pushbutton is n pressed.

15. NOT Gate Application – Example 2
If the power is “on”
(1) and the pressure
switch is not closed
(0), the warning
indicator will be “on”
Low-pressure
indicating circuit
When the pressure
rises to close the
pressure switch, the
warning indicator
will be switched "off"

16. NAND Function The NAND gate functions like an AND gate with an
inverter connected to its output.
The only time the NAND gate output is 0 is when
all inputs are binary 1.

17. NOR Function The NOR gate functions like an OR gate with an
inverter connected to its output.
The only time the NAND gate output is 1 is when
all inputs are binary 0.

18. XOR (exclusive-OR) Function
The XOR function has
two inputs and one output.
The output of this gate is HIGH only when one input or
the other is HIGH, but not both.
It is commonly used for comparison of two binary
numbers.

19. 1. The two binary states can be defined as:
“high” or “low”
“on” or “off”
1” or “0”
all of these
2. A gate can have one or more outputs but
only one input. (True/False)

20. 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)

21. 6. With an AND gate, if any input is 0, the output will be 0
6. With an AND gate, if any input is 0, the output will be (True/False)
7. The symbol shown is that of a(an)
_________ .
AND gate
OR gate
NAND gate
inverter

22. 8. Which of the following gates is commonly used
for the comparison of two binary numbers?
NAND
NOR
XOR
NOT
9. The basic rule for an XOR function is that if
one or the other, but not both, inputs are 1 the
output is 1. (True/False)
10. A NAND gate is an AND gate with an inverter
connected to the output. (True/False)

23. Gate Boolean EquationsY
AND
Y = A B
Gate
Boolean Equation OR A B Y
Y = A + B
NOT A Y
Y = A

24. Boolean Equation – Example 1
Each logic function can be
expressed in terms of a
Boolean expression

25. Boolean Equation – Example 2
Any combination of control can be expressed in terms of a Boolean equation AB
Y = AB + C
A + B
Y = (A + B) C

26. Boolean Equation – Example 2AB
Y = AB + C
A + B
Y = (A + B) C

27. Circuit Development Using A Boolean Expression – Example 1
1. AND gate with Input A and B
2. OR gate with Input C an output from previous AND gate.

28. Circuit Development Using A Boolean Expression – Example 2
AND gate with Input B and C

29. Producing A Boolean Expression From A Given
Circuit – Example 1

30. Producing A Boolean Expression From A Given
Circuit – Example 2
Logic equation: Y = AB + AB

31. Hard Wired versus Programmed Logic
The term hardwired logic refers to logic control
functions that are determined by the way devices
are interconnected.
Hardwired logic can be
implemented using relays
and relay ladder schematics.
Hardwired logic is fixed:
it is changeable only by altering
the way devices are connected.

32. Hardwired Stop/Start Motor Control Circuit
Ladder rung
Ladder rail
Control scheme is drawn
between two vertical
supply lines.

33. Programmed Stop/Start Motor Control Circuit
A rung is the contact symbolism required to control
an output. Each rung is a combination of input
conditions connected from left to right with the
symbol that represents the output at the far right.
The input and output field devices remain the same
as those required for the hardwired circuit.
The instructions used are the relay equivalent of
normally open (NO) and normally closed (NC)
contacts and coils

34. Hard Wired versus Programmed Logic
Example 4-1

35. Hard Wired versus Programmed Logic
Example 4-2

36. Hard Wired versus Programmed Logic
Example 4-3

37. Hard Wired versus Programmed Logic
Example 4-4

38. Hard Wired versus Programmed Logic
Example 4-5

39. Hard Wired versus Programmed Logic
Example 4-6

40. Hard Wired versus Programmed Logic
Example 4-7

41. Hard Wired versus Programmed Logic
Example 4-8

42. Hard Wired versus Programmed Logic
Example 4-9

43. Selecting Word-Level Logic Instructions
If you want to know when matching bits in two different
words are both ON use the AND instruction.
If you want to know when one or both matching bits in
two different words are ON use the OR instruction.
If you want to know when one or the other bit of
matching bits in two different words is ON use the
XOR instruction.
If you want to reverse the status of bits in a word use
the NOT instruction.

44. Programmed AND Instruction
There is a 1 at
B3:10 only
when Source A
and B bits are
1 and input A
is true

45. Programmed AND Instruction
There is a 1 at
B3:10 only
when Source A
and B bits are
1 and input A
is true

46. Programmed OR Instruction
There is a 1 at
B3:20 when
either or both
the Source
A or B bits are 1

47. Programmed XOR Instruction
There is an
output only
when Source A
and B bits are
different

48. Programmed NOT Instruction
The bits from
B3:9 are sent
to B3:10 and
inverted when
input A is true

49. 11. Hardwired logic is changeable only by altering
the way devices are connected.
(True/False)
12. Each programmed rung is a combination of
input conditions connected from left to right with
the symbol that represents the output at the far
right.
(True/False)

50. 13. Which gate logic shown represents the Boolean
equation: ( A + B ) C = Y
(a)
(b)
(c)
(d)

51. 14. The correct Boolean equation for the combination logic gate circuit shown is:
a. Y = A B C D c. Y = ( A + B ) ( C + D )
b. Y = ( AB ) + ( CD ) d. Y = ( AB ) + ( CD )

52. 15. The correct Boolean equation for the combination logic gate circuit shown is:
a. Y = ( A + B + C ) D c. Y = ( AB + C ) D
b. Y = ( A + B ) ( C + D ) d. Y = ( ABC ) D

53. 16. The correct Boolean equation for the combination logic gate circuit shown is:
a. Y = A B C c. Y = A + B + C
b. Y = ( A B ) C d. Y = ( AB ) + ( BC )

54. 17. The correct Boolean equation for the ladder
logic program shown is:
a. Y = (A B) + (CD) c. Y = A + B + C + D
b. Y = (A+B ) (C+D) d. Y = ABCD

55. 18. The correct Boolean equation for the ladder
logic program shown is:
a. Y = (A B) + (CD) c. Y = A + B + C + D
b. Y = AB (C+D) d. Y = ABC + D

56. 19. If you want to know when matching bits in two different words are both "on", you would use the _____ logic instruction.
a. AND c. XOR
b. OR d. NOT
20. If you want to reverse the state of bits in a word, you would use the ______ logic instruction.
a. AND c. XOR
b. OR d. NOT