1. Copyright © 2002 Delmar Thomson Learning Chapter 4 Number Systems

2. Copyright © 2002 Delmar Thomson Learning Objectives  Identify the commonly used number systems used in PLCs.  Convert binary data to decimal.  Examine how data is stored in PLC data tables.  Describe how BCD field devices interface.

3. Copyright © 2002 Delmar Thomson Learning Why Do I Need to Understand How Data Is Represented?  In order to install, program,maintain, and troubleshoot today’s PLCs, you must understand the different methods by which internal data is represented.

4. Copyright © 2002 Delmar Thomson Learning Number Systems Typically Used with PLCs

5. Copyright © 2002 Delmar Thomson Learning We Use Words to Represent Information  Our words are groups of characters grouped together to represent something.  The words we use are of different lengths:  Controller  The  Monday

6. Copyright © 2002 Delmar Thomson Learning We Use Symbols Called Numbers to Represent Data  Everyday numbers are decimal. 12,345

7. Copyright © 2002 Delmar Thomson Learning Computers Do Not Understand  Computers do not understand the words and numbers humans use.  Computers have their own language called binary.

8. Copyright © 2002 Delmar Thomson Learning Binary Language  Binary information is also represented in groups of characters.  A group of BInary digiTs called bits can be organized into words.  Binary bits consist of only two characters: 1 and 0

9. Copyright © 2002 Delmar Thomson Learning Binary Words  16 bits grouped together is called a word.  A binary would might look like: 1010 1010 1010 1010 1010

10. Copyright © 2002 Delmar Thomson Learning Decimal Numbers  Ten Digits 0,1,2,3,4,5,6,7,8,9  Base or radix 10  Weights 1, 10, 100, 1000 …..

11. Copyright © 2002 Delmar Thomson Learning Decimal Number System

12. Copyright © 2002 Delmar Thomson Learning Sixteen-Bit Binary Word Bit Weighting

13. Copyright © 2002 Delmar Thomson Learning Comparison of Decimal to Binary Numbers

14. Copyright © 2002 Delmar Thomson Learning Decimal Place Value Equivalent

15. Copyright © 2002 Delmar Thomson Learning Comparison of Decimal to Binary Numbers

16. Copyright © 2002 Delmar Thomson Learning Four-Digit BCD Thumb-Wheel

17. Copyright © 2002 Delmar Thomson Learning Comparison of BCD to Decimal and Binary Numbers

18. Copyright © 2002 Delmar Thomson Learning Single-Digit BCD Thumb-Wheel Interfaced to a PLC

19. Copyright © 2002 Delmar Thomson Learning Binary-Coded Decimal Number Bit Patterns

20. Copyright © 2002 Delmar Thomson Learning Two-Digit BCD Thumb-Wheel Interface

21. Copyright © 2002 Delmar Thomson Learning BCD Invalid Codes

22. Copyright © 2002 Delmar Thomson Learning Thumb-Wheel Dialed to 11

23. Copyright © 2002 Delmar Thomson Learning Thumb-Wheel Dialed to 743

24. Copyright © 2002 Delmar Thomson Learning Output Module Connected to Seven-Segment Display

25. Copyright © 2002 Delmar Thomson Learning Decimal 0 through 7 Represented with Binary Bits

26. Copyright © 2002 Delmar Thomson Learning Octal Number System Place Values

27. Copyright © 2002 Delmar Thomson Learning Decimal, Hexadecimal, and BCD Comparisons

28. Copyright © 2002 Delmar Thomson Learning Place Values of Hexadecimal