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Arithmetic Instructions

Chapter 06 and supplemental material

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Arithmetic Instructions

Mnemonic Name Mnemonic NameADD 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

SQRSquare Root(SQRT, Siemens)

LOG Log to the Base 10

SCP Scale with Parameters SIN Sine

SCL Scale TAN Tangent

ABS Absolute Value XPYX to the Power of Y(EXPT, Siemens)

CPT Compute NEG Negate

We will only be learning about the instruction shown in red

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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

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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 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

3. Source B can be a program constant and Source A 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.

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. In ControlLogix a tag of type SINT, INT, DINT or REAL.

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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)

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Arithmetic Instructions

Arithmetic instructions can be conditional or unconditional: Conditional – Input logic determines when the instruction executes. Unconditional – Instruction executes every scan.

Conditional

0 AddSource A Vessel_A_Level 0Source B Vessel_B_Level 0Dest Total_of_Batch 0

ADD

Unconditional

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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.

0 AddSource A Vessel_A_Level 367Source B Vessel_B_Level 780Dest Total_of_Batch 1147

ADD

sumsignedbit

BatchofTotalLevelBVesselLevelAVessel

nDestinatioSourceBSourceA

321147780367

______

signedbitisroLogixP

sumsignedbit

NNN

nDestinatioBSourceASource

32

16850650200

1:72:70:7

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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)

Bit is set to a (1) if the result or value after a math, 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.

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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)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:N Sign (S)

Bit is set to a (1) if the result or value after a math, 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.

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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.

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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.

al

numnum

sumnumnum

OUTINnININ

Re850650200

65002,20001

0201

21

The Enable Out (ENO)

will set to a logic 1 when the instruction is true and has not generated and math errors.

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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.

0

End of batches sensor

1 = End of BatchesEnd_of_Batches<Local:3:I.Data.2>

SubtractSource A Num_of_Batches.ACC 50Source B Bad_Batches.ACC 2Dest Total_of_Batch 48

SUB

differencebit

BatchofTotalACCBatchesBadACCBatchesofNum

DestSourceBSourceA

3248250

__._.__

)difference signedbit-32 (LogixPro

)difference signedbit-(16 20- 85 - 65

5:N7 2.ACC:C5 - 1.ACC:C5

nDestinatio B Source- A Source

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Siemens Subtract (SUB) Instruction The SUB instructions subtracts the value in IN1 from the value in

IN2 and stores the difference in the OUT.

48250

22,501

21

ININ

estotalBatchbadBatchesesnumOfBatch

OUTININ The Enable Out (ENO) will set to a logic 1 when the instruction is true and has not generated and math errors.

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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.

nDestinatio in storedbit-(16 10,000 20* 500

4.PRE:T4 20* 3.PRE:T4

onDesitinati B * Source A Source

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When performing integer division, the DIV instruction performs long division. Therefore:

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.

SLC 500 Divide (DIV) Instruction

122/5 ofremainderawith

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SLC500 Divide (DIV) Instruction

nDestinatioinstoredquotientroundedbit

NNN

nDestinatioBSourceASource

1632/5

23:79:7/7:7

/

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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.

0

Execute the MUL instruction

1 = ExecuteMultiply

<Local:3:I.Data.12>MultiplySource A 2 Source B Thumb_Value 6000Dest Actual_Value 12000

MUL

12000 6000* 2

ueActual_Val eThumb_Valu* 2

nDestinatio B * Source A Source

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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.

0

Execute the MUL instruction

1 = ExecuteMultiply

<Local:3:I.Data.12>DivideSource A Raw_Thumb_Value 10Source B Thumb_Value 6Dest Actual_Value 1

DIV

1 6 / 10

ueActual_Val eThumb_Valu / ValueRaw_Thumb_

nDestinatio B Source/ A Source

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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.

126*2

6humbValuet

eactualValu thumbValue* 2

OUT IN2* IN1 The Enable Out (ENO) will set to a logic 1 when the instruction is true and has not generated and math errors.

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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.

1 6 / 10

6thumbValue10,luerawThumbVa

eactualValu thumbValue / luerawThumbVa

OUT IN2 / IN1

The Enable Out (ENO)

will set to a logic 1 when the instruction is true and has not generated and math errors.

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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 ModuloSource A Thumb_Value 7Source B 2 Dest Actual_Value 1

MOD

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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.

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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.

bit)-(16 4 3:N7

16 3:N7

4:N10 3:N7

bit)-(32 4 eHypostenus

16 Hypotenuse

esSumOfSquar Hypotenuse

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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.

4 lvesselLeve

16 lvesselLeve

evelcylVesselL lvesselLeve

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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 = ExecuteMultiply

<Local:3:I.Data.12>ClearDest Actual_Value 0

CLR

ControlLogix Example

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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.

50 50-

5.PRE:T21 68:N10

nDestinatio Source

50 50-

ABS_Dest ABS_Source

nDestinatio Source

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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.

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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.

1 X To Power Of YSource X Vessel_B_Level 2Source Y Thumb_Value 6Dest Actual_Value 64

XPY

642

___6

_

ValueActualLevelBVessel ValueThumb

ControlLogix Example Shown

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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.

642

6,26

thumbValueevelcylVesselL

lvesselLeveevelcylVesselL thumbValue

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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

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Compute (CPT), CALCULATE InstructionSupplement 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.

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Compute (CPT) InstructionSupplement to Textbook

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

NOTBit-by-bit inversion of a binary value

Trig Functions

SIN, COS, ATN, ACS, ASN, TAN

XORBit-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)

Instructions that can be used in the Expression

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Compute (CPT) Instruction, ControlLogixSupplement to Textbook

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.

525

169

43

43

22

22

hypotenuse

hypotenuse

ThensideBandsideAIf

hypotenusesideBsideA

ControlLogix Example Shown

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Compute (CPT) InstructionSupplement to Textbook

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)Sets based on the results of the last instruction executed in the expression.

S:0/3 or S:N Sigh (S)Sets based on the results of the last instruction executed in the expression.

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CALCULATE Instruction, SiemensSupplement to Textbook

The CALCULATE instruction can be conditional or unconditional.

525

169

43

43

21

22

22

hypotenuse

hypotenuse

ThensideBandsideAIf

hypotenuseININ

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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

FunctionsABS, 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

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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

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Order of Precedence

Examples of Order of Precedence:

Equation to Evaluate25 * 2 + 4 / 2 * 6 – 45 + 16 / 8

Evaluate from left to rightDivision and multiplication have higher precedence than

addition and subtraction25 * 2 = 50

4 / 2 * 6 = 2 * 6 = 1216 / 8 = 2

50 + 12 – 45 + 262 – 45 + 217 + 2 = 19

25 * 2 + 4 / 2 * 6 – 45 + 16 / 8 = 19