Appendix
G
Numbering
S
ystems
G--6
Numbering Systems
DL105 PLC User Manual, 3rd Edition
Real (Floating Point) Numbering System
The terms Real and floating--point both describe IEEE--754 floating point arithmetic.
This standard specifies how single precision (32 bit) and double precision (64 bit)
floating point numbers are to be represented as well as how arithmetic should be
carried out on them. Most PLCs use the 32--bit format for floating point (or Real)
numbers which will be discussed here.
Real (Floating Point 32) Bit Pattern
Bit #
31
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
Sign
Exponent
Mantissa
Bit #
15
14 13 12 11 10 9
8
7
6
5
4
3
2
1
0
Mantissa (continues from above)
Table 6
Floating point numbers, which
Direct
LOGIC PLCs use, have three basic
components: sign, exponent and mantissa. The 32 bit word required for the IEEE
standard floating point numbers is shown in Table 6. It is represented as a number
bits from 0 to 31, left to right. The first bit (31) is the sign bit, the next eight bits (30--23)
are the exponent bits and the final 23 bits (22--0) are the fraction bits. In summary:
The sign bit is either “0” for positive or “1“ for negative;
The exponent uses base 2;
The first bit of the mantissa is typically assumed to be “1.fff“, where “f“ is the field of
fraction bits.
The Internet can provide a more in--depth explanation of the floating point
numbering system. One website to look at is:
http://www.psc.edu/general/software/packages/ieee/ieee.php
Summary of Contents for DL105
Page 2: ...DL105 PLC User Manual Manual Number D1 USER M...
Page 308: ...1B DL105 Error Codes In This Appendix Error Code Table...
Page 314: ...1C Instruction Execution Times In This Appendix Introduction Instruction Execution Times...
Page 324: ...1D Special Relays In This Appendix DL105 PLC Special Relays...
Page 327: ...1E PLC Memory In This Appendix DL105 PLC Memory...
