1. Chapter 4
Number Systems

2. 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. 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. Number Systems Typically Used with PLCs

5. 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. We Use Symbols Called Numbers to Represent Data
Everyday numbers are decimal. 12,345

7. Computers Do Not Understand
Computers do not understand the words and numbers humans use.
Computers have their own language called binary.

8. 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. Binary Words 16 bits grouped together is called a word.
A binary word might look like:

10. Decimal Numbers Ten digits Base or radix Weights 0,1,2,3,4,5,6,7,8,910
Weights
1, 10, 100, 1000 …..

11. Decimal Number System

12. Sixteen-Bit Binary Word Bit Weighting

13. Comparison of Decimal to Binary Numbers

14. Decimal Place Value Equivalent

15. Comparison of Decimal to Binary Numbers
Powers of two 24 23 22 21 20
Place value 16 8 4 2 1
A: Decimal 1=
B: Decimal 2=
C: Decimal 3=
D: Decimal 4=
E: Decimal 5=
F: Decimal 6=
G: Decimal 7=
H: Decimal 8=
I: Decimal 21=

16. Four-Digit BCD Thumb-Wheel

17. Comparison of BCD to Decimal and Binary Numbers

18. Single-Digit BCD Thumb-Wheel Interfaced to a PLC

19. Binary-Coded Decimal Number Bit Patterns

20. Two-Digit BCD Thumb-Wheel Interface

21. BCD Invalid Codes

22. Thumb-Wheel Dialed to 11

23. Thumb-Wheel Dialed to 743

24. Output Module Connected to Seven-Segment Display

25. Decimal 0 through 7 Represented with Binary Bits

26. Octal Number System Place Values

27. Decimal, Hexadecimal, and BCD Comparisons

28. Place Values of Hexadecimal