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The most frequently asked question by students who are studying automation is: Why do we have to learn number systems?

Well...let's think of it this way. If you were visiting a forign country you would want to learn a-bit of the language that is spoken in that country. Phrases like, where is the rest room? Can you direct me to the train station? Think of PLC/PAC's as a forign country and the language spoken is numbers.

PLC/PAC's use four number systems:

(Click the number system for more information
and converting to other number systems.)

- Decimal
- The decimal number system is the number system we use everyday. 'Deci' means 10, therefore there are 10 valid numbers, 0 through 9. Decimal is a 'base 10' number system.
- Binary
- The binary number system is the number system used by computers, PLC/PAC's and any other equipment and devices that are digital. 'Bi' means 2, therefore there are 2 valid numbers, 0 and 1. Binary is a 'base 2' number system.
- Octal
- The octal number system is a number system used by early PLC/PAC's. 'Octa' means 8, therefore there 8 valid numbers, 0 through 7. There are no 8's or 9's in this number system. Octal is a 'base 8' number system.
- Hexadecimal
- The Hexadecimal number system is a number system used by all PLC/PAC's, computers and other equipment and devices that are digital. 'Hexa' means 16, therefore there are 16 valid numbers, 0 through 9 and A through F. Hexadecimal is a 'base 16' number system.
- BCD Numbers
- Binary Coded Decimal (BCD) is not really a number system. It is a method to make human machine interface (HMI) easier by representing the decimal number 0 - 9 in a 4-bit binary code. If you understand the hexadecimal numbers, you will understand BCD.
- Negative Numbers
- Most PLC/PAC's store negative numbers in 2's compliment. The 2's compliment method of conversion is detailed in this topic.
- Number Conversions
- Modern PLC/PAC programming software allows the user to change the base of the number being displayed. The term 'radix' is used for changing the base of the number system. Even though the software does the conversion I'm from the school that believes a person should know how to do an operation before using the tool that does it for you. This section explains how to convert from one number system base to any other.

The PLC/PAC Tutorial ⇔ All rights reserved
⇔ Copyright © 2009

John G. (Skip) Todora ⇔ Late updated: November 11, 2009

John G. (Skip) Todora ⇔ Late updated: November 11, 2009