Modbus protocol description and set-up – KROHNE ALTOSONIC V12 EN User Manual

Page 124

MODBUS PROTOCOL DESCRIPTION AND SET-UP

124

ALTOSONIC V12

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04/2013 - 4002643502 - MA ALTOSONIC V12 R02 en

10.6.4 Double precision floating point (64 bit), transmit sequence

Double precision floating-point numbers are stored in 64-bit registers, represented using the
IEEE 754 encoding. In IEEE 754-2008 the 64-bit base 2 format is officially referred to as binary64.
It was called double in IEEE 754-1985.

The IEEE 754 standard specifies a binary64 as having:

• Sign bit: 1 bit
• Exponent width: 11 bits
• Significant (also known as mantissa) precision: 53 (52 explicitly stored)

The true significant (mantissa) includes an implicit leading bit with value 1 unless the exponent
is stored with all zeros. Thus only 52 bits of the significand (mantissa) appear in the memory
format but the total precision is 53 bits (equivalent to log10(253) ≈ 16 decimal digits). The bits are
laid out as follows:

Double precision bits

Double precision bits 2

Example

The double number 4.125000001862645 will give the IEEE representation:

double number example

A positive sign

A biased exponent of 1025 (401 hexadecimal) is exp. 2
Mantissa = 4 + 1/8 + 1/536870912. Note that the first bit is not stored!
Doubles could be transmitted in two ways. The transmit order in both modes:

Sign +
(Biased)
Exponent

Exponent +
Mantissa

Mantissa 6

Mantissa 5

SEEE EEEE

EEEE MMMM

MMMM

Mantissa 4

Mantissa 3

Mantissa 2

Mantissa 1

MMMM

Sign

Exponent

Mantissa

100 0000 0001

(1)0000 1000 0000 0000 0000 0000

0000 0010 0000 0000 0000 0000

0000