Math Instructions
Program logic controller
Math Instructions
Objective
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Math Instructions
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Math Instructions
Math instructions, like data manipulation instructions, enable the
programmable controller to take on more of the qualities of a
conventional computer. The PLC’s math functions capability
allows it to perform arithmetic functions on values stored in
memory words or registers.
Example
assume you are using a counter to keep track of the number of parts
manufactured, and you would like to display how many more parts must be
produced in order to reach a certain quota. This display would require the data in
the accumulated value of the counter to be subtracted from the quota required.
Other applications include combining parts counted, subtracting detected
defects, and calculating run rates. Depending on what type of processor is used,
various math instructions can be programmed.
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The basic four mathematical functions performed by PLCs are:
Addition
The capability to add
one piece of data to
another.
Subtraction
capability to subtract
one piece of data
from another.
Multiplication
Division
The capability to
multiply one piece of
data by another.
The capability to
divide one piece of
data by another.
The Compute/Math menu tab for the SLC 500 PLC and its associated RSLogix software.
CPT
(Compute)—
Evaluates an
expression
and stores
the result in
the
destination.
ADD (Add)—
Adds source
A to source B
and stores
the result in
the
destination.
SUB
(Subtract)—
Subtracts
source B
from source
A and stores
the result in
the
destination.
MUL
(Multiply)—
Multiplies
source A by
source B and
stores the
result in the
destination.
DIV (Divide)—
Divides source
A by source B
and stores the
result in the
math register
and
destination.
SQR (Square
Root)—
Calculates the
square root of
the source and
places the
integer result
in the
destination.
Program logic controller
NEG
(Negate)—
Changes the
sign of the
source and
places it in the
destination.
TOD (To
BCD)—
Converts a 16bit integer
source value
to BCD and
stores it in the
math register
or the
destination.
Math Instructions
FRD (From
BCD)—
Converts a
BCD value in
the math
register or the
source to an
integer and
stores it in the
destination.
CPT (compute)
When CPT instruction is executed, then copy, arithmetic,
logical, or conversion operation residing in the expression
field of this instruction is performed and the result is sent to
the destination. The execution time of a CPT instruction is
longer than that of a single arithmetic operation and uses
more instruction words.
The main advantage of the compute instruction is that it allows you to enter quite
complex expressions in one instruction.
a ladder rung used to convert a Fahrenheit temperature to a Celsius temperature
using a single RSLogix 5000 compute instruction.
In this example a temperature of
140°F is programmed into N7:5 of
the Expression and the computed
value of 60°C appears in the Result.
Program logic controller
Math Instructions
Addition Instruction
Most math instructions take two input values,
perform the specified arithmetic function, and
output the result to an assigned memory location.
The program of Next Figure illustrates how the ADD instruction can be used to
add the accumulated counts of two up-counters. This application requires a pilot
light to come on when the sum of the counts from the two counters is equal to or
greater than 350.
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Subtraction Instruction
The SUB (subtract) instruction is an output instruction that subtracts one value from
another and stores the result in the destination address. When rung conditions are true,
the subtract instruction subtracts source B from source A and stores the result in the
destination.
The program of next Figure shows how the SUB function can be used to
indicate a vessel overfill condition.
This application requires an alarm to sound when a supply system leaks 5 lb
or more of raw material into the vessel after a preset weight of 500 lb has
been reached.
Program logic controller
Math Instructions
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Math Instructions
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Multiplication Instruction
The multiply (MUL) instruction is an
output instruction that multiplies two
values and stores the result in the
destination address.
The program of next figure is an example of how the MUL instruction is used as
part of an oven temperature control program.
• In this example, the set-point temperature is 400°F.
• Therefore, the electric heaters will be turned on when the temperature of the oven drops to
less than 396°F and stay on until the temperature rises above 404°F.
• If the set-point is changed to 100°F, the deadband remains at ±1 percent, with the lower limit
being 99°F and the upper limit being 101°F.
• The number stored in word N7:1 represents the upper temperature limit, and the number
stored in word N7:2 represents the lower limit.
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Division Instruction
The divide (DIV) instruction divides
the value in source A by the value in
source B and stores the result in the
destination and math register.
DIV instruction
to calculate the
that
results
dividing source
source B.
used
value
from
A by
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The program of figure is an example of
how the DIV function is used as part of
a program to convert Celsius
temperature to Fahrenheit.
• The thumbwheel switch connected to the input module indicates
Celsius temperature.
• The program is designed to convert the recorded Celsius
temperature in the data table to Fahrenheit values for display.
• The following conversion formula forms the basis
for the program:
• In this example, a current temperature reading of 60°C is assumed.
• The PLC processor carries out its internal operations using binary
numbers and the FRD instruction is used to convert the 16-bit integer
values from the thumbwheel switch into BCD values.
• The MUL instruction multiplies the temperature (60°C) by 9 and stores
the product (540) in address N7:0.
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Other Word-Level Math Instructions
Square root (SQR) instruction
Negate (NEG) instruction
This math function changes the sign of the source
value from positive to negative
Clear (CLR) instruction
Program logic controller
Math Instructions
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.
convert from BCD (FRD) instruction
is used to convert 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
Scale data (SCL) and Scale with
Parameters (SCP) instruction
make conversions to analog input and output values to
ensure correct interpretation and processing. As a result,
data must be scaled, or resized, before it can be used by a
PLC control algorithm or output to a field device.
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y = mx + b
Where: y is the output , m is the scaling rate, x is the input, b is the offset
Scaling rate (m) = (scaled Max − scaled Min) / (input Max − input Min)
Offset (b) = (scaled Min) − (input Min x m)
The execution of the instruction can be summarized as follows:
• A strain-gage pressure transducer is connected to input I:1.0.
• The gage measures pressure from 0 to 1000 psi and provides an analog output of 0 to 10V.
• The unscaled range is 0 to 32,767, and the output is loaded into N7:20.
• When executed, the SCP instruction places a number between 0 and 1000 into N7:20 (destination) based
on the input signal (0 to 10V) coming from the transducer into the analog input module.
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The execution of the instruction can be summarized as follows:
• A proportional control valve is connected to the PLC output O:1.0.
• A 4 to 20 mA signal operates the valve from closed to 100% open.
• The percent open is in location N7:21.
• The PLC analog module provides a 4 to 20 mA output signal for a number between from 6,242 to 31,208.
• The SCP directs analog output O:1.0 to provide a 4 to 20 mA signal, which is scaled to the valve position
based on a number between 0 and 100.
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