Summary

ProSoft/ModBus/Rockwell Automation PLC-5 utility

Filling in some details related to this ProSoft KnowledgeBase article:

• http://www.prosoft-technology.com/kb/article.php?id=449

Emulate conversion from a one-element, IEEE-754 32-floating point file and a two-element, 16-bit integer file, and vice versa. By emulate is meant to show what integer values result from a floating point value, and vice versa.

N.B. does not work for 0.0 and other special values (Inf, NaN, etc.).

Usage

Open floatingbits.html in a Web Browser; file

./scripts/jquery-1.9.1.min.js

may need to be accessible and in the sub-directory scripts/, which is a sibling of floatingbits.html.

Details

Here's the full conversion from 28876 and 16709 to floating-point (FP) value 12.34.

Let's say LSW and MSW are in Binary file 4 with 2 elements (like your B3 example)

LSW is B4:0 = 16709

MSW is B4:1 = 28836

The bits, from MSBit to LSB, LSW then MSW, are

1. B4:0/15 => 1 bit for sign (set=1 if FP is negative, unset=0 if FP is positive)

• for 16709, B4:0/15 is unset, so the number is positive (so far, so good)
• negative numbers will either have B4:0 greater than 32767 (interpreting 16-bits as an UN-signed Int); or have B4:0 as a negative number (interpreting 16-bits as a signed Int).

2. B4:0/14 to B4:0/7 => 8 bits evaluated as an 8-bit integer (1-255; exponent value of zero has a special meaning), minus 127 to give base-two exponent

• Int(16709 / 128) - 127 = 130 - 127 = 3
• 2 to the 3rd power = 8, so the number is between 8 and 16 (8*2) (still so far so good).

3. B4:0/6 to B4:0/0 and B4:1/15 to B4:1/0 => (7 + 16 =) 23 bits to represent mantissa-equivalent = bits after binamal (analogous to decimal) point with an implied leading 1 bit set before the binamal point

• 16 LSBits (B4:1) are 28836
• 1+7 most significant bits:
  • 7 bits from LSW = 16709 % 128 = 16709 - (130 * 128) = 69
  • Implicit leading 1 bit: add 128
  • 69 + 128 = 197 ((197 / 128) * 8 = 12.3125, close to 12.34, still so far so good)
• To combine them, left-shift the MSBits by 16-bits and add to the LSBits:
  • (197 * 65536) + 28836 = 12939428
• and divide that by 2^23 (= 8388608) to shift the binamal point 23 places to the left;
  • 12939428 / 8388608 = 1.5425

Finally, combining everything: + 1.5425 * (2^3) = 1.5425 * 8 = 12.34

QED?

So, for the general case using Integer files, assuming LSW and MSW = N4:0 and N4:1, UN-signed 16-bit integers

SIGN: +1 if N4:0/1 is unset; -1 if set

EXPONENT: int( (N4:0 - (int(N4:0/32768) * 32768) / 128) - 127

MANTISSA: 65536.0 * (int( (N4:0 - (int(N4:0/32768) * 32768) - (128 * (EXPONENT+126))) + N4:1

FP = [SIGN] MANTISSA * 2^EXPONENT

• N.B. implicit leading 1-bit in MANTISSA is provided by adding +126 instead of +127 in MANTISSA formula above

Manifest

• floatingbits.html HTML/Javascript converter

• scripts/jquery-1.9.1.min.js jQuery if web version not found

• Integer_to_IEEE754_Convert.xlsx Original workbook converter

• Integer_to_IEEE754_Convert_FV4.ods LibreOffice spreadsheet converter

• Integer_to_IEEE754_Convert_FV4.xls eXcel XP copy of .ods spreadsheet

• bits.py Python script converter

• Makefile To make ZIP file for distribution

• readme.md This file