KROHNE OPTISONIC V6 Modbus User Manual
Page 14
2011-07-19
OPTISONIC_V6_Modbus_6.doc
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The IEEE 754 standard specifies a binary64 as having:
•
Sign bit: 1 bit
•
Exponent width: 11 bits
•
Significand (also known as mantissa) precision: 53 (52 explicitly stored)
The true significand (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(2
53
) ≈ 16 decimal digits). The bits are laid out as follows:
Sign + (Biased) Exponent
Exponent + Mantissa
Mantissa 6
Mantissa 5
SEEE EEEE
EEEE MMMM
MMMM MMMM
MMMM MMMM
Mantissa 4
Mantissa 3
Mantissa 2
Mantissa 1
MMMM MMMM
MMMM MMMM
MMMM MMMM
MMMM MMMM
Example
The double number 4.125000001862645 will give the IEEE representation:
Sign
Exponent
Mantissa
0
100 0000 0001
(1)0000 1000 0000 0000 0000 0000 0000 0010 0000 0000 0000 0000 0000
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:
IEEE 754
(1)
40
h
(2)
10
h
(3)
80
h
(4)
00
h
(5)
00
h
(6)
20
h
(7)
00
h
(8)
00
h
Normal mode
(1)
40
h
(2)
10
h
(3)
80
h
(4)
00
h
(5)
00
h
(6)
20
h
(7)
00
h
(8)
00
h
Reversed mode
(3)
80
h
(4)
00
h
(1)
40
h
(2)
10
h
(7)
00
h
(8)
00
h
(5)
00
h
(6)
20
h
6.5
Long long (64 bit integer), Transmit Sequence
Example
64 bit integer value 4.616.330.355.545.210.880 (= 4010 8000 0020 0000 hexadecimal).
64 bit integers
could be transmitted in two ways. The transmit order in both modes:
Normal mode
(1)
40
h
(2)
10
h
(3)
80
h
(4)
00
h
(5)
00
h
(6)
20
h
(7)
00
h
(8)
00
h
Reversed mode
(3)
80
h
(4)
00
h
(1)
40
h
(2)
10
h
(7)
00
h
(8)
00
h
(5)
00
h
(6)
20
h
6.6
Maximum number requested items
The maximum amount of data that can be sent in a single response limits the amount of items that can be
requested in a single query. The table below shows the maximum number of items per data type:
Data type
Number of items
Boolean
2000
Integer (16 bit)
125
Long integer (32 bit)
62
Float (32 bit floating point)
62
Double (64 bit floating point)
31
Long long (64 bit integer)
31