12 chapter06 math_instructions_fa14

Arithmetic Instructions
Chapter 06 and supplemental material
Northampton Community College 1

Mnemonic Name Mnemonic Name
ADD Addition SWP Swap
SUB Subtraction ASN Arc Sine
MUL Multiply ACS Arc Cosine
DIV Divide ATN Arc Tangent
DDV Double Divide (SLC500) COS Cosine
CLR Clear LN Natural Log
SQR
Square Root
(SQRT, Siemens)
LOG Log to the Base 10
SCP Scale with Parameters SIN Sine
SCL Scale TAN Tangent
ABS Absolute Value XPY
X to the Power of Y
(EXPT, Siemens)
CPT Compute NEG Negate
We will only be learning about the instruction shown in red

Allen Bradley Arithmetic Instructions
 Math instructions are output instructions, therefore they are
placed against the right power rail.
 The ControlLogix processor allows math instructions to be
placed in series on the right side of the rung. (Not in this course)
 The ADD, SUB, MUL and DIV instructions have three
parameters:
 Source A
 Source B
 Destination
RSLogix 500 and LogixPro ControlLogix

Basic Arithmetic Instructions
 The ADD, SUB, MUL and DIV instructions have three parameters:
 Source A
 Source B
 Destination
 These parameters have the following rules.
1. Source A and Source B
 In the SLC500 can be any valid word level address of type INT or FLOAT.
 In LogixPro can be any valid word level address of type INT.
 In ControlLogix a tag of type SINT, INT, DINT or REAL.
2. Source A can be a program constant and Source B
 In ControlLogix a tag of type SINT, INT, DINT or REAL
3. Source B can be a program constant and Source A
4. Source A and Source B cannot both be program constants.
5. The Destination is always
 In the SLC500 a valid word level address of type INT or FLOAT .
 In LogixPro a valid word level address of type INT.

Siemens Arithmetic Instructions
 The Siemens processor allows math instructions to be
placed in series on the rung.
 The ADD, SUB, MUL and DIV instructions have at least six
parameters:
 Instruction Data Type
 Enable (EN)
 Enable Out (ENO)
 OUT
 IN1, IN2, (INn when the yellow star is present)

Arithmetic instructions can be conditional or unconditional:
 Conditional – Input logic determines when the instruction executes.
 Unconditional – Instruction executes every scan.
Conditional
Unconditional
ADD
Add
Source A Vessel_A_Level
0
Source B Vessel_B_Level
0
Dest Total_of_Batch
0

Allen Bradley Addition (ADD) Instruction
 The ADD instructions adds the value in Source A to the value in
Source B and stores the sum in the Destination.
Source A  SourceB 
Destination
N N N
7 : 0 7 : 2 7 :1
 bit signed sum

 
200 650 850 16
  
LogixPro is 32

bit signed
0 Add
ADD
Source A Vessel_A_Level
367
Source B Vessel_B_Level
780
Dest Total_of_Batch
1147
SourceA  SourceB 
Destination
Vessel _ A _ Level  Vessel _ B _ Level 
Total _ of _
Batch
 bit signed sum
367 780 1147 32
  

SLC500 Arithmetic Status Bits
 There are four arithmetic status bits. All of the arithmetic instructions share the
same four status bits.
 These bits will contain the status of the last math instruction that is executed.
 These bits are located in the Status File (S2) and are described as follows (Not
available in the LogixPro Simulator):
Status Bit Name Description
S:0/0 Carry (C)
Bit is set to a (1) if a carry is generated; otherwise it is
cleared (0). (It is for you to determine how this bit
works)
S:0/1 Overflow (V)
Bit is set to a (1) if the result or value of the math
instruction does not fit into the designated destination.
Value is smaller than -32,768 or larger than 32,767;
otherwise it is cleared (0).
S:0/2 Zero (Z)
Bit is set to a (1) if the result or value after a math,
move or logic instruction is zero; otherwise it is cleared
(0).
S:0/3 Sign (S)
move or logic instruction is a negative (less than zero)
value; otherwise it is cleared (0). This bit is not to be
confused with the sign bit (15) of a 16-bit word.

ControlLogix Arithmetic Status Bits
 There are four arithmetic status bits. All of the arithmetic instructions share the
same four status bits.
 These bits will contain the status of the last math instruction that is executed.
Status Bit Name Description
S:C Carry (C)
Bit is set to a (1) if a carry is generated; otherwise it is
cleared (0). (It is for you to determine how this bit
works)
S:V Overflow (V)
Bit is set to a (1) if the result or value of the math
instruction does not fit into the designated destination.
Min. and max. values are determined by the data type
of the tag; otherwise it is cleared (0).
S:Z Zero (Z)
move or logic instruction is zero; otherwise it is cleared
(0).
S:N Sign (S)
move or logic instruction is a negative (less than zero)
value; otherwise it is cleared (0). This bit is not to be
confused with the sign bit (31) of a 32-bit word.

Arithmetic Status Bit Example of Operation
The status bits will
contain the status of
the last math
instruction that is
executed. Therefore,
in the example to the
right, that status bits
will contain the status
of the Square Root
SQR instruction.

Siemens Addition (ADD) Instruction
 The ADD instructions adds the value in IN1 to the value in INB to
the value in INn and stores the sum in the OUT tag.
   The Enable Out (ENO)
IN 1 IN 2
INn OUT
num 01  num 02

sum
num num
01  200, 02 
650
 al 
200  650 
850 Re
will set to a logic 1 when
the instruction is true
and has not generated
and math errors.

Allen Bradley Subtract (SUB) Instruction
 The SUB instructions subtracts the value in Source A from the
value in Source B and stores the difference in the Destination.
Source A - Source B Destination
C5 : 1.ACC - C5 : 2.ACC N7 : 5
65 - 85 
- 20 (16 - bit signed difference )
(LogixPro 32 - bit signed difference )
SourceA SourceB Dest
Num _ of _ Batches . ACC Bad _ Batches . ACC Total _ of _
Batch
0
End of batches
sensor
1 = End of Batches
End_of_Batches
<Local:3:I.Data.2>
Subtract
Source A Num_of_Batches.ACC
50
Source B Bad_Batches.ACC
2
Dest Total_of_Batch
48
SUB
 bit dif ference
  
 
 
50 2 48 32



Siemens Subtract (SUB) Instruction
 The SUB instructions subtracts the value in IN1 from the value in
IN2 and stores the difference in the OUT.
IN 1 IN 2
OUT The Enable Out (ENO)
numOfBatches  badBatches 
totalBatches
 
IN IN
1  50, 2 
2
50  2 
48
and math errors.

SLC 500 Multiply (MUL) Instruction
The MUL instruction multiplies the value in Source A by the
value in Source B and stores the 16-bit product in the
Destination.
If the values being multiplied will result in a product outside
the range -32,768 to 32,767, use Floating Point addresses.
Source A * Source B 
Desitination
T4 : 3.PRE * 20 
T4 : 4.PRE
500 * 20 
10,000 (16 -bit stored in Destination

SLC 500 Divide (DIV) Instruction
When performing integer division, the DIV instruction
performs long division. Therefore:
5/ 2  2 witha remainderof 1
The instruction divides the value in Source A by the value
in Source B and stores the results as follows:
 The rounded 16-bit quotient is stored in the Destination.
 When dividing 5 / 2, the destination will most likely a value of 3.

SLC500 Divide (DIV) Instruction
Source A /
SourceB Destination
N N N
7 : 7 / 7 :9 
7 : 23

 bit rounded quotient stored inDestination
5/ 2 3 16
 

ControlLogix Multiply (MUL) Instruction
The MUL instruction multiplies the value in Source A by the
value in Source B and stores product in the Destination.
Source A * Source B Destination
2 * Thumb_Value Actual_Value
0
Execute the MUL
instruction
1 = Execute
Multiply
<Local:3:I.Data.12>
Multiply
Source A 2
Source B Thumb_Value
6000
Dest Actual_Value
12000
MUL
2 * 6000 
12000



ControlLogix Divide (DIV) Instruction
 The ControlLogix DIV instruction divides the value of Source A by the
value of Source B and stores the quotient in the Dest. See the next
slide for rounding and truncating of the Dest.
Source A / Source B Destination
Raw_Thumb_Value / Thumb_Value Actual_Value
0
Execute the MUL
instruction
1 = Execute
Multiply
<Local:3:I.Data.12>
Divide
Source A Raw _Thumb_Value
10
Source B Thumb_Value
6
Dest Actual_Value
1
DIV
10 / 6 
1



Siemens Multiply (MUL) Instruction
 The Siemens MUL instruction multiplies the value of IN1 by the value of
IN2 by the value of INn and stores the product in the OUT.
IN1 * IN2 OUT The Enable Out (ENO)
2 * thumbValue actualValue
thumbValue 6
2*6 12



and math errors.

Siemens Divide (DIV) Instruction
 The Siemens DIV instruction divides the value of IN1 by the value of
IN2 and stores the quotient in the OUT.
IN1 / IN2 OUT
 The Enable Out (ENO)
rawThumbValue / thumbValue 
actualValue
rawThumbValue 10, thumbValue 6
10 / 6 
1
 
and math errors.

ControlLogix Modulo (MOD) Instruction
The MOD instruction divides the value stored in Source A by
the value in Source B and places the remainder in the Dest.
The Source A, Source B and the Dest follow the same rules
as the ADD, SUB, MUL and DIV instructions.
0 Modulo
MOD
Source A Thumb_Value
7
Source B 2
Dest Actual_Value
1
푆표푢푟푐푒퐴
푆표푢푟푐푒퐵
= 퐷푒푠푡 (푟푒푚푎푖푛푑푒푟)
푇ℎ푢푚푏_푉푎푙푢푒
2
= 퐴푐푡푢푎푙_푉푎푙푢푒
푇ℎ푢푚푏_푉푎푙푢푒 = 7
7
2
= 1

Siemens Modulo (MOD) Instruction
The MOD instruction divides the value stored in IN1 by the
value in IN2 and places the remainder in the OUT.
퐼푁1
퐼푁2
= 푂푈푇
푒푣푒푛푂푟푂푑푑
2
= 푟푒푚푎푖푛푑푒푟
푒푣푒푛푂푟푂푑푑 = 12
12
2
= 0

Allen Bradley Square Root (SQR) Instruction
 The SQR instruction has two parameter; Source and Destination.
 Both parameters must be word level addresses. In the SLC500 the value
can be of type INT or FLOAT and in the ControlLogix the value can be a
tag of type SINT, INT, DINT or REAL.
 The SQR instruction takes the square root of the value stored in the
Source and stores the result in the Destination.
N7 : 3 
N10 : 4
N7 : 3 
16
N7 : 3 
4 (16 - bit)
Hypotenuse 
SumOfSquares
Hypotenuse 
16
Hypostenuse 
4 (32- bit)

Siemens Square Root (SQR) Instruction
 The SQR instruction has two parameter; IN and OUT.
 Both parameters must be word level addresses.
 The SQR instruction takes the square root of the value stored in the IN
and stores the result in the OUT.
vesselLevel 
cylVesselLevel
vesselLevel 
16
vesselLevel 
4

ControlLogix Clear (CLR) Instruction
The CLR instruction has one parameter; Destination.
In the SLC500, the Destination can be any valid word level
address and in the ControlLogix it can be a tag of type
SINT, INT, DINT or REAL.
When the rung containing the CLR instruction is true, the
value stored in the word level address referenced in the
Destination is cleared; set to zero (0).
1
Execute the MUL
instruction
1 = Execute
Multiply
<Local:3:I.Data.12>
Clear
Dest Actual_Value
0
CLR
ControlLogix Example

Absolute Value (ABS) Instruction
(Not available in LogixPro)
 The ABS instruction has two parameters; Source and Destination.
 In the SLC500 the Source and Destination can be any valid word level
address. In the ControlLogix they can be a tag of type SINT, INT, DINT or
REAL.
 When the rung containing the ABS instruction is true, the instruction takes
the absolute value of the value stored in the Source word and places the
resultant value in the Destination word.
Source 
Destination
N10 : 68 T21: 5.PRE
- 50 
50

Source 
Destination
ABS_Source ABS_Dest
- 50 
50


Siemens CLR and ABS
Siemens does not have a Clear (CLR) instruction.
The Siemens Absolute value instruction is not available in
ladder logic. It is only available in structured text.

ControlLogix X To Power of Y (XPY) Instruction
(Not available in LogixPro)
 The XPY instruction has three parameters; Source A, Source B and
Destination.
 The rules for the parameters are the same as for the ADD, SUB, MUL and
DIV instructions.
 The instruction raises the value stored in Source A to the power of the
value stored in Source B and stores the result in the Destination.
XPY
1 X To Pow er Of Y
Source X Vessel_B_Level
2
Source Y Thumb_Value
6
Dest Actual_Value
64
ControlLogix Example Shown
Vessel _ B _ Level Thumb _
Value
 Actual _
Value 6
2 
64

Siemens X To Power of Y (EXPT) Instruction
 The XPY instruction has three parameters; IN1, IN2 and OUT.
 The instruction raises the value stored in IN1 to the power of the value
stored in IN2 and stores the result in OUT.
cylVesselLevel vesselLevel thumbValue
cylVesselLevel thumbValue
6 
2 64

 
2, 6

Compute (CPT) Instruction, Allen Bradley
(Not available in LogixPro Supplement to Textbook)
 The Compute (CPT) instruction is an output instruction. It has two
parameters:
 Destination
 Expression
 In the SLC500 the Destination can be any valid word level address. In
the ControlLogix it can be a tag of type SINT, INT, DINT or REAL.
 The Expression can contain any valid expression (equation) to be
solved.
 In the SLC500 series the CPT instruction is only available on:
 SLC 5/03 OS302 or higher
 SLC 5/04 OS401 or higher
 SLC 5/05 all operating systems

Compute (CPT), CALCULATE Instruction
Supplement to Textbook
The Allen Bradley Compute (CPT) and the Siemens
CALCULATE instruction can perform any or all of the
following operations:
 Copy
 Arithmetic
 Logical
 Conversion
The operation is defined in the Expression and the result of
the Expression is stored in the address referenced in the
Destination.

Compute (CPT) Instruction
Instructions that can be used in the Expression
Instruction Explanation Instruction Explanation
+ Addition AND Bit-by-bit AND of two values
- Subtraction TOD Convert 16-bit Integers to BCD
* Multiplication FRD Convert BCD to 16-bit Integers
|
Division in the SLC500 (This is the
pipe character. It is a vertical line).
LN Calculates Natural Log
/ Division in the ControlLogix ABS Takes the absolute value
SQR Square Root (SQRT, Siemens) DEG Convert radians to degrees
-
Negate. (Same as using the NEG
instruction)
RAD Convert degrees to radians
NOT
Bit-by-bit inversion of a binary
value
Trig
Functions
SIN, COS, ATN, ACS, ASN, TAN
XOR
Bit-by-bit eXclusive OR of two
values
LOG Calculates log base 10
OR Bit-by-bit OR of two values **
Raise a number to a power
(SQR, Siemens)

Compute (CPT) Instruction, ControlLogix
The CPT instruction can be
conditional or unconditional.
The Expression is an
equation of zero or more
lines, with up to 28
characters per line and up
to 255 characters.
 2 2

sideA sideB hypotenuse
If sideA and sideB Then
2 2
3 4
 
 
 
9 16
 
25 5
3 4

hypotenuse
hypotenuse
ControlLogix Example Shown

Compute (CPT) Instruction
The arithmetic status bits update as shown in the table:
With this bit: The Processor:
S:0/0 or S:C Carry (C)
Sets based on the results of the last
instruction executed in the expression.
S:0/1 or S:V Overflow (V)
Sets anytime an overflow occurs during
the evaluation of the expression.
S:0/2 or S:Z Zero (Z)
S:0/3 or S:N Sigh (S)

CALCULATE Instruction, Siemens
The CALCULATE
instruction can be
conditional or
unconditional.
 2 2

IN 1  IN 2

hypotenuse
If sideA and sideB Then
2 2
3 4
 
 
9 16
 
25 5
3 4

hypotenuse
hypotenuse

Order of Precedence
 When parentheses are not used to control the order in which elements
of a mathematical equation should be executed, there is an order of
precedence to the math operators. This order and the direction they are
evaluated are listed below.
Operator Symbol Direction Evaluated
Parentheses ( )
In order from inner pairs to
outer pairs
Functions
ABS, ACS, ASN, ATN, COS,
DEG, FRD, LN, LOG, RAD, SIN,
SQR, TAN, TOD, TRN
In the order as per
instruction
Exponentiation ** Left to Right
Negation - Left to Right
Math *, |, /, MOD Left to Right
Math +, - Left to Right
Comparison
LES, GRT, LEQ, GEQ, EQU,
NEQ, LIM
Left to Right
Logical AND, OR, NOT, XOR Right to Left

Order of Precedence
Examples of Order of Precedence:
Equation to Evaluate
15 + 60 / 3 – 4 * 5 + 7
Evaluate from left to right
Division and multiplication have higher precedence than
addition and subtraction
60 / 3 = 20
4 * 5 = 20
15 + 20 – 20 + 7
15 + 7 = 22
 15 + 60 / 3 – 4 * 5 + 7 = 22

Order of Precedence
Examples of Order of Precedence:
Equation to Evaluate
25 * 2 + 4 / 2 * 6 – 45 + 16 / 8
Evaluate from left to right
Division and multiplication have higher precedence than
addition and subtraction
25 * 2 = 50
4 / 2 * 6 = 2 * 6 = 12
16 / 8 = 2
50 + 12 – 45 + 2
62 – 45 + 2
17 + 2 = 19
 25 * 2 + 4 / 2 * 6 – 45 + 16 / 8 = 19

12 chapter06 math_instructions_fa14

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12 chapter06 math_instructions_fa14