Petruzella F.D. Programmable Logic Controllers

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Math Instructions Chapter 11 233

• The following conversion formula forms the basis

for the program:

F 5

(

× C

)

1 32

• In this example, a current temperature reading of

60°C is assumed.

• The MUL instruction multiplies the temperature

(60°C) by 9 and stores the product (540) in address

N7:0.

• Next, the DIV instruction divides 5 into the 540 and

stores the answer (108) in address N7:1.

• Finally, the ADD instruction adds 32 to the value of

108 and stores the sum (140) in address O:13.

• Thus 60°C 5 140°F.

11. 6 Other Word-Level Math

Instructions

The program of Figure11-14 is an example of the square

root (SQR) instruction. The operation of the logic rung

can be summarized as follows:

• When input switch SW is closed the SQR instruc-

tion is executed.

• The number whose square root we want to deter-

mine (144) is placed in the source.

• The function calculates the square root and places it

(12) in the destination.

• If the value of the source is negative, the instruction

will store the square root of the absolute (positive)

value of the source at the destination.

Figure 11-12 DIV instruction used to calculate the value that results

from dividing source A by source B.

Ladder logic program

OutputInput

PL1

DIV

DIVIDE

Source A

Source B

Destination

N7:0

120

N7:1

N7:5

EQU

EQUAL

Source A

Source B

N7:5

PL1

Ladder logic programInput

Thumbwheel

switch

Output

MUL

MULTIPLY

Source A

Source B

Destination

Ι:012

N7:0

540

DIV

DIVIDE

Source A

Source B

Destination

N7:0

540

N7:1

108

ADD

Source A

Source B

Destination

N7:1

108

O:013

140

Ι:012

O:013

0 6 0

LED

Display

FahrenheitCelsius

14 0

Figure 11-13 Program for converting Celsius temperature

to Fahrenheit.

Figure 11-14 SLC 500 SQR (square root) instruction.

Ladder logic program Input

SQR

SQUARE ROOT

Source A

Destination

N7:101

144

N7:105

( 144 = 12)

√

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234 Chapter 11 Math Instructions

Figure11-17 is an example of the TOD instruction. The

operation of the logic rung can be summarized as follows:

• When input switch SW is closed the TOD instruc-

tion is executed.

• The binary bit pattern at the source address N7:23 is

converted into a BCD bit pattern of the same deci-

mal value at the destination address O:20.

• The source displays the value 10, which is the

correct decimal value; however, the destination

displays the value 16.

• The processor interprets all bit patterns as binary;

therefore the value 16 is the binary interpretation of

the BCD bit pattern.

• The bit pattern for 10 BCD is the same as the bit

pattern for 16 binary.

The convert from BCD (FRD) instruction is used to con-

vert binary-coded decimal (BCD) values to integer values.

This instruction could be used to convert data from a BCD

external source, such as a BCD thumbwheel switch, to the

binary format in which the processor operates. The program

of Figure11-18 is an example of the FRD instruction. The

operation of the logic rung can be summarized as follows:

• When input switch SW is closed the FDR instruc-

tion is executed.

• The BCD bit pattern stored at the source address

I:30 is converted into a binary bit pattern of the same

decimal value at the destination address, N7:24.

The program of Figure 11-15 is an example of the

negate (NEG) instruction. This math function changes

the sign of the source value from positive to negative.

The operation of the logic rung can be summarized as

follows:

• When input switch SW is closed the NEG instruc-

tion is executed.

• The positive value 101 stored at the source address

N7:52 is negated to 2101 and stored in destination

address N7:53.

• Positive numbers will be stored in straight binary

format, and negative numbers will be stored as 2’s

complement.

The program of Figure11-16 is an example of the clear

(CLR) instruction. The operation of the logic rung can be

summarized as follows:

• When input switch SW is closed the CLR instruc-

tion is executed.

• Upon execution it sets all bits of a word to zero.

• In this example it changes the value of all bits stored

in the destination address N7:22 to 0.

The convert to BCD (TOD) instruction is used to

convert 16-bit integers into binary-coded decimal

(BCD) values. This instruction could be used when

transferring data from the processor (which stores data

in binary format) to an external device, such as an LED

display, that functions in BCD format. The program of

Figure 11-15 SLC 500 NEG (negate) instruction.

Ladder logic program Input

NEG

NEGATE

Source A

Destination

N7:52

101

N7:53

–101

Figure 11-16 SLC 500 CLR (clear) instruction.

N7:22

0000000000000000

Ladder logic program Input

CLR

CLEAR

Destination

Ladder logic program Input

TOD

TO BCD

Source

Destination

N7:23

O:20

Figure 11-17 SLC 500 TOD (convert to BCD) instruction.

Figure 11-18 SLC 500 FRD (convert from BCD)

instruction.

Ladder logic program Input

FRD

FROM BCD

Source

Destination

I:30

N7:24

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Math Instructions Chapter 11 235

data in  le address N7:25 to the data stored in  le

address N7:50 and store the result in  le address

N7:100.

• The rate per scan is set at All, so the instruction

goes to completion in one scan.

The program of Figure11-21 is an example of the  le

subtract function of the FAL instruction. The operation of

the logic rung can be summarized as follows:

• When input switch SW is closed the rung goes true

and the processor subtracts a program constant

(255) from each word of  le address N10:0 and

The scale data (SCL) instruction is used to allow very

large or very small numbers to be enlarged or reduced by

the rate value. When rung conditions are true, this instruc-

tion multiplies the source by a speci ed rate. The rounded

result is then added to an offset value and placed in the

destination. The program of Figure11-19 is an example

of the SCL instruction. The operation of the logic rung

can be summarized as follows:

• When input switch SW is closed the SCL instruc-

tion is executed.

• The number 100 stored at the source address, N7:0,

is multiplied by 25,000, divided by 10,000, and

added to 127.

• The result, 377, is placed in the destination address,

N7:1.

You can use SCL instruction to scale data from your

analog module and bring it into the limits prescribed by the

process variable or another analog module. For instance,

you can use the SCL instruction to convert a 4–20 mA

input signal to a PID process variable, or to scale an ana-

log input to control an analog output.

11.7 File Arithmetic Operations

File arithmetic functions include  le add,  le subtract,

 le multiply,  le divide,  le square root,  le convert from

BCD, and  le convert to BCD. The  le arithmetic and

logic (FAL) instruction can combine an arithmetic opera-

tion with  le transfer. The arithmetic operations that can

be implemented with the FAL are ADD, SUB, MULT,

DIV, and SQR.

The  le add function of the FAL instruction can be

used to perform addition operations on multiple words.

The program of Figure11-20 is an example of the  le add

function of the FAL instruction. The operation of the logic

rung can be summarized as follows:

• When input switch SW is closed the rung goes true

and the expression tells the processor to add the

Figure 11-19 SLC 500 SCL (scale) instruction.

Ladder logic program Input

SCL

SCALE

Source

Rate (/10000)

Offset

Destination

N7:0

100

25000

127

N7:1

377

Ladder logic program Input

FAL

FILE ARITH/LOGICAL

Control

Length

Position

Mode

Destination

Expression

#N7:25 + #N7:50

R6:1

All

#N7:100

234

1256

N7:25

N7:28

= N7:100

= N7:103

+ N7:50

+ N7:53

456

100

256

1712

177

#N7:25 #N7:50 #N7:100

Figure 11-20 SLC 500 ﬁ le add function of the FAL

instruction.

Figure 11-21 SLC 500 ﬁ le subtract function of the FAL

instruction.

680

950

100

N10:0

N10:3

= N7:255

= N7:258

– 255 425

695

–235

–155

#N10:0 #N7:255

Ladder logic program Input

FAL

FILE ARITH/LOGICAL

Control

Length

Position

Mode

Destination

Expression

#N10:0 – 255

R6:5

#N7:255

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236 Chapter 11 Math Instructions

• The rate per scan is set at All, so the instruction

goes to completion in one scan.

The program of Figure11-23 is an example of the  le

divide function of the FAL instruction. The operation of

the logic rung can be summarized as follows:

• When input switch SW is closed the rung goes true

and the data in  le address F8:20 is divided by the

data in  le address F8:100, with the result stored in

element address F8:200.

• The mode is Incremental, so the instruction operates

on one set of elements for each false-to-true transi-

tion of the instruction.

stores the result at the destination  le address,

N7:255.

• The rate per scan is set at 2, so it will take 2 scans

from the moment the instruction goes true to com-

plete its operation.

The program of Figure11-22 is an example of the  le

multiply function of the FAL instruction. The operation of

the logic rung can be summarized as follows:

• When input switch SW is closed the rung goes true

and the data in  le address N7:330 is multiplied by

the data in element address N7:23, with the result

stored at the destination  le address N7:500.

Figure 11-22 SLC 500 ﬁ le multiply function of the FAL

instruction.

240

–78

321

N7:330

N7:333

= N7:500

= N7:503

N7:23 100

2000

24000

–7800

32100

#N7:330 #N7:500N7:23

Ladder logic program Input

FAL

FILE ARITH/LOGICAL

Control

Length

Position

Mode

Destination

Expression

#N7:330

N7:23

R6:8

All

#N7:500

Figure 11-23 SLC 500 ﬁ le divide function of the FAL

instruction.

Ladder logic program Input

FAL

FILE ARITH/LOGICAL

Control

Length

Position

Mode

Destination

Expression

#F8:20 / #F8:100

R6:7

Incremental

F8:200

100

1.33

586

F8:20

F8:23

= F8:200÷ F8:100

F8:103

1000

1.5

0.1

#F8:20 #F8:100 F8:200

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Math Instructions Chapter 11 237

1. Explain the function of math instructions as applied

to the PLC.

2. Name the four basic math functions performed by

PLCs.

3. What standard format is used for PLC math

instructions?

4. Would math instructions be classi ed as input or

output instructions?

5. With reference to the instruction of Figure11-24 ,

what is the value of the number stored at source B

if N7:3 contains a value of 60 and N7:20 contains a

value of 80?

6. With reference to the instruction of Figure11-25 ,

what is the value of the number stored at the desti-

nation if N7:3 contains a value of 500?

7. With reference to the instruction of Figure11-26 ,

what is the value of the number stored at the des-

tination if N7:3 contains a value of 40 and N7:4

contains a value of 3?

8. With reference to the instruction of Figure11-27 ,

what is the value of the number stored at the

destination if N7:3 contains a value of 15 and N7:4

contains a value of 4?

9. With reference to the instruction of Figure11-28 ,

what is the value of the number stored at N7:20 if

N7:3 contains a value of 2345?

10. With reference to the instruction of Figure11-29 ,

what will be the value of each of the bits in word

B3:3 when the rung goes true?

11. With reference to the instruction of Figure11-30 ,

what is the value of the number stored at N7:101?

12. With reference to the instruction of Figure11-31 ,

list the values that will be stored in  le #N7:10

when the rung goes true.

Figure 11-24 Instruction for Question 5.

ADD

Source A

Source B

Destination

N7:3

N7:4

N7:20

Figure 11-25 Instruction for Question 6.

SUB

SUBTRACT

Source A

Source B

Destination

N7:3

338

N7:20

Figure 11-26 Instruction for Question 7.

DIV

DIVIDE

Source A

Source B

Destination

N7:3

N7:4

N7:20

Figure 11-27 Instruction for Question 8.

MUL

MULTIPLY

Source A

Source B

Destination

N7:3

N7:4

N7:20

Figure 11-28 Instruction for Question 9.

NEG

NEGATE

Source

Destination

N7:3

N7:20

Figure 11-29 Instruction for Question 10.

CLR

CLEAR

Destination

B3:3

0000111100001111

Figure 11-30 Instruction for Question 11.

SQR

SQUARE ROOT

Source A

Destination

N7:101

N7:105

FAL

FILE ARITH/LOGICAL

Control

Length

Position

Mode

Destination

Expression

#N11:0  10

R6:0

All

#N7:10

328

150

File #N11:0

Figure 11-31 Instruction for Question 12.

CHAPTER 11 REVIEW QUESTIONS

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238 Chapter 11 Math Instructions

(3) N7:1

(4) Source B of the GEQ instruction

d. Will output PL1 be energized at this point?

Why?

2. Answer each of the following with reference to the

over ll alarm program shown in Figure11-33 .

a. Assume that the vessel is  lling and has reached

the 300-lb point. State the status of each of the

logic rungs (true or false) at this point.

b. Assume that the vessel is  lling and has reached

the 480-lb point. State the value of the number

stored in each of the following words at this

point:

(1) I:012

(2) N7:1

c. Assume that the vessel is  lled to a weight of

502 lb. State the status of each of the logic rungs

(true or false) for this condition.

1. Answer each of the following with reference to the

counter program shown in Figure11-32 .

a. Assume the accumulated count of counters C5:0

and C5:1 to be 148 and 36, respectively. State

the value of the number stored in each of the fol-

lowing words at this point:

(1) C5:0.ACC

(2) C5:1.ACC

(3) N7:1

(4) Source B of the GEQ instruction

b. Will output PL1 be energized at this point?

Why?

c. Assume the accumulated count of counters C5:0

and C5:1 to be 250 and 175, respectively. State

the value of the number stored in each of the fol-

lowing words at this point:

(1) C5:0.ACC

(2) C5:1.ACC

CHAPTER 11 PROBLEMS

Figure 11-32 Program for Problem 1.

Inputs

OutputLadder logic program

C5:0

350

CTU

COUNT-UP COUNTER

Counter

Preset

Accumulated

C5:1

350

CTU

COUNT-UP COUNTER

Counter

Preset

Accumulated

PL1

C5:0.ACC

C5:1.ACC

N7:1

ADD

Source A

Source B

Destination

Reset

C5:0

GEQ

GREATER THAN OR EQUAL

Source A

Source B

N7:1

350

RES

C5:1

RES

PL1

Reset

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Math Instructions Chapter 11 239

c. Assume that the set-point temperature is 600°F

and the thermocouple input module indicates a

temperature of 608°F. What is the status (energized

or not energized) of each of the following outputs?

(1) PL1

(2) PL2

(3) Heater

4. With reference to the Celsius to Fahrenheit con-

version program shown in Figure11-35 , state the

value of the number stored in each of the following

words for a thumbwheel setting of 035:

a. I:012

b. N7:0

c. N7:1

d. O:013

5. Design a program that will add the values stored

at N7:23 and N7:24 and store the result in N7:30

whenever input A is true, and then, when input B is

true, will copy the data from N7:30 to N7:31.

6. Design a program that will take the accumulated

value from TON timer T4:1 and display it on a

4-digit, BCD format set of LEDs. Use address

d. Assume that the vessel is  lled to a weight of

510 lb. State the value of the number stored in

each of the following words for this condition:

(1) I:012

(2) N7:1

e. With the vessel  lled to a weight of 510 lb, state

the status of each of the logic rungs (true or

false).

3. Answer the following with reference to the tem-

perature control program shown in Figure11-34 .

a. Assume that the set-point temperature is 600°F.

At what temperature will the electric heaters be

turned on and off?

b. Assume that the set-point temperature is 600°F

and the thermocouple input module indicates a

temperature of 590°F. What is the value of the

number stored in each of the following words at

this point?

(1) I:012

(2) I:013

(3) N7:0

(4) N7:1

(5) N7:2

Figure 11-33 Program for Problem 2.

Ladder logic program

Full

Fill

solenoid

Fill

solenoid

Full

Filling

Outputs

Inputs

Weight

transducer

(All 16 bits)

SUB

SUBTRACT

Source A

Source B

Destination

GEQ

GREATER THAN OR EQUAL

Source A

Source B

GEQ

GREATER THAN OR EQUAL

Source A

Source B

N7:1

Start

Ι:012

Stop

Ι:012

500

Full

Fill

solenoid

Alarm

Start

Stop

Filling

Ι:012

500

N7:1

Fill

solenoid

Alarm

Full

Filling

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240 Chapter 11 Math Instructions

• Multiply the value in N7:3 by 25 and store the

result in N7:4.

• Divide the value in N7:4 by 35 and store the

result in F8:0.

8. a. There are three part conveyor lines (1-2-3) feed-

ing a main conveyor. Each of the three conveyor

lines has its own counter. Construct a PLC pro-

gram to obtain the total count of parts on the

main conveyor.

b. Add a timer to the program that will update the

total count every 30 s.

O:023 for the LEDs. Include the provision to

change the preset value of the timer from a set of

4-digit BCD thumbwheels when input A is true.

Use address I:012 for the thumbwheels.

7. Design a program that will implement the follow-

ing arithmetic operation:

• Use a MOV instruction and place the value 45 in

N7:0 and 286 in N7:1.

• Add the values together and store the result in N7:2.

• Subtract the value in N7:2 from 785 and store the

result in N7:3.

Figure 11-34 Program for Problem 3.

Ladder logic program

ON/OFF

PL1 PL2

Heater

PL2

PL1

MUL

MULTIPLY

Source A

Source B

Destination

Ι:012

400

0.0100000

N7:0

ADD

Source A

Source B

Destination

Ι:012

400

N7:0

N7:1

404

SUB

SUBTRACT

Source A

Source B

Destination

Ι:012

400

N7:0

N7:2

396

LES

LESS THAN

Source A

Source B

Ι:013

N7:2

396

GRT

GREATER THAN

Source A

Source B

Ι:013

N7:1

404

Inputs

ON/OFF

TWS

Thermocouple

input

Ι:013

Ι:012

PL1

PL2

Heater

Outputs

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Math Instructions Chapter 11 241

10. With reference to the math instruction program

shown in Figure11-37 , when the input goes

true, what value will be stored at each of the

following?

a. N7:3

b. N7:4

c. N7:5

d. N7:6

11. Two part conveyor lines, A and B, feed a main

conveyor line M. A third conveyor line, R,

removes rejected parts a short distance away from

the main conveyor. Conveyors A, B, and R have

parts counters connected to them. Construct a PLC

program to obtain the total parts output of main

conveyor M.

12. A main conveyor has two conveyors, A and B,

feeding it. Feeder conveyor A puts six-packs of

canned soda on the main conveyor. Feeder con-

veyor B puts eight-packs of canned soda on the

main conveyor. Both feeder conveyors have coun-

ters that count the number of packs leaving them.

Construct a PLC program to give a total can count

on the main conveyor.

9. With reference to math instruction program shown

in Figure11-36 , when the input goes true, what

value will be stored at each of the following?

a. N7:3

b. N7:5

c. F8:1

Figure 11-35 Program for Problem 4.

Ladder logic programInput

Thumbwheel

switch

Celsius

Fahrenheit

Output

MUL

MULTIPLY

Source A

Source B

Destination

Ι:012

N7:0

DIV

DIVIDE

Source A

Source B

Destination

N7:0

N7:1

ADD

Source A

Source B

Destination

N7:1

O:013

Ι:012

O:013

LED

Display

Figure 11-36 Program for Problem 9.

MUL

MULTIPLY

Source A

Source B

Destination

N7:3

N7:4

N7:5

ADD

Source A

Source B

Destination

N7:1

208

N7:2

114

N7:3

DIV

DIVIDE

Source A

Source B

Destination

N7:5

5.000000

F8:1

Input

Figure 11-37 Program for Problem 10.

Input

MUL

MULTIPLY

Source A

Source B

Destination

N7:3

N7:4

SUB

SUBTRACT

Source A

Source B

Destination

N7:1

N7:2

N7:3

ADD

Source A

Source B

Destination

N7:4

N7:5

SQR

SQUARE ROOT

Source

Destination

N7:5

N7:6

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242

Sequencer and Shift

Chapter Objectives

After completing this chapter, you will be able to:

12.1 Identify and describe the various forms of mechanical

sequencers and explain the basic operation of each

12.2 Interpret and explain information associated

with PLC sequencer output, compare, and load

instructions

12.3 Compare the operation of an event-driven and a time-

driven sequencer

12.4 Describe the operation of bit and word shift registers

12.5 Interpret and develop programs that use shift registers

This chapter explains how the PLC sequencer

and shift register functions operate and how

they can be applied to control problems. The se-

quencer instruction evolved from the mechanical

drum switch, and it can handle complex sequenc-

ing control problems more easily than does the

drum switch. Shift registers are often used to

track parts on automated manufacturing lines by

shifting either status or values through data ﬁ les.

Image Used with Permission of Rockwell Automation, Inc.

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