Introduction to Industrial Automation

Figure A.7  Conversion of an octal number to a decimal.

Octal number

2 5 7

Binary

number

0 1

1

1

1 1 1

0

0

2

8

Figure A.8  Conversion of an octal number to binary.

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Appendix A 

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415

A.6   Hexadecimal Arithmetic System

Another arithmetic system that is widely used in PLCs and PCs is the hexadecimal arithmetic 

system, also often referred to as HEX. This system has a base 16, which means that it uses 16-digit 

symbols that take decimal values from 0 to 15. But because it will create confusion if a hexadeci-

mal digit consisted of two numbers, the digits from 10 to 15 are represented by the letters of the 

alphabet A to F, as shown in Table A.1. For example, the hypothetical number 15

16

 is not clear 

what expresses, because may be the hexadecimal 15 (equivalent decimal value 15) or two discrete 

digits, the hexadecimal 1 and the hexadecimal 5, which have an equivalent decimal value of 21. 

Although the use of letters in the hexadecimal system seems complicated at first sight, the hexa-

decimal code is the most appropriate for the digital representation of numbers. The reason is that 

it is possible with two hexadecimal digits to represent all the decimal numbers from 0 to 255 (0 to 

FF), while in a binary arithmetic system 8 binary bits or 1 byte are required.

The position weighting values of the hexadecimal system are derived in a similar way to that 

applied to binary and decimal systems. Starting from the first right position with the null power 

value of 16 (16

0

), the value at each position of a hexadecimal digit rises to the left of the LSB by 

a power of 16. Converting a decimal number to a hexadecimal one becomes with subsequent