Introduction to Industrial Automation

Table A.2  Gray Code and Binary Equivalents

Gray Code

Binary Number

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

1

0

0

1

1

0

0

1

0

0

0

1

0

0

0

1

1

0

1

1

0

0

1

0

0

0

1

1

1

0

1

0

1

0

1

0

1

0

1

1

0

0

1

0

0

0

1

1

1

1

1

0

0

1

0

0

0

1

1

0

1

1

0

0

1

1

1

1

1

1

0

1

0

1

1

1

0

1

0

1

1

1

0

1

0

1

1

0

0

1

0

1

1

1

1

0

1

1

0

0

1

1

1

1

0

1

0

0

0

1

1

1

1

---

419

Appendix B: Analog I/O 

Values Scaling

B.1   PLC Analog I/O Values Scaling

During the programming task of an automation application, including the processing of analog val-

ues, it is necessary to address some secondary issues, such as the violation of limits of an analog input, 

the scaling-conversion of analog I/O range into units of physical magnitude (also called engineering 

units), the overflow or underflow of digital arithmetic limits (>32768 or <−32768), etc. The correct or 

incorrect operation of the PLC program depends on proper knowledge of these issues. In the operation 

manuals with the technical characteristics of the PLC’s analog I/O modules, one can find the required 

information concerning the digital representation of analog values for all the standard analog ranges 

that an analog module can accept, the measurement or overload limits of the A/D or D/A converter, 

and also the manner of address. Here, reference will be provided only to the analog value scaling that 

is illustrated in Figure B.1, and expresses the need for a human operator to use engineering units.

Let’s assume that a temperature transducer has an analog output 0–10 V DC that is connected 

to an analog input of a PLC. The output voltage of the transducer is proportional to the tempera-

ture range 100 °C to 500 °C. The transducer measures the temperature of a thermal process, which 

should fluctuate from 250 °C to 300 °C by applying the required control. Figure B.2 illustrates the 

whole scaling procedure, particularly the linear relation between the input (voltage) and the out-

put (arithmetic value that expresses °C). In the diagram, the maximum voltage 10 V corresponds 

to the arithmetic value 32767, but in some PLCs, this may be 27648 or another arithmetic limit, 

depending on the existence or absence of an overflow or over-range detection. The input/output 

linear relation is expressed by the following equations:

 

Scaled Output Value = (Input Voltage Slope)+

×

Offset

 (B.1)

 

Slope = Max Scaled Value Min Scaled Value

Max In

–

pput Value Min Scaled Value

–

 (B.2)

 

Offset = Min Scaled Value (Min Input Slope)

–

×

 (B.3)

What is needed in the sequence, is to determine which voltage values correspond to the tem-

perature limits (250 °C and 300 °C) that are controlled in order not to be violated. The calculation 

is based on Equation B.1, which is solved for “Input Voltage”,

 

Input Voltage = (Scaled Output Value Offset)/Sl

–

oope

 (B.4)

---

420

 

◾

  Appendix B

Applying Equation B.4 for the two temperature limit values, it is derived that,

 

Low Limit = (250 100)/(400/32767) = 12287

–

and

 

High Limit = (300 100)/(400/32767) = 16393

–

In some PLCs, system function blocks perform the required scaling operation. Otherwise, 

based on the above scaling equations, one has to program either the control of the temperature or 

any other simpler application as the indication of temperature in a digital panel, and then incor-

porate the required instructions to the whole PLC program of the automation.

PLC

Scaling

010010100110

Indication

0–200 kg

Voltage

0–10 V

Weight

0–200 kg

Scaling to

physical unit

0–200 kg

Binary number

expressing voltage

0-32767

Load cell

230 V 230 V 230 V 0–10 V

16

16

16

4

DO

DO

DO

AI

C

P

U

PS

C

P

1

C

P

2

B

156 kg

Figure B.1  The scaling of an analog value is a necessary procedure to convert numeric data