1. Converting floating-point numbers from the hexadecimal into the decimal format
The following diagram shows the arrangement of bits of IEEE floating-point numbers. Bit 31 = sign, bits 23 to 30 = exponent and bits from 0 to 22 = mantisse.
Bit
31 24 23 16 15 8 7 0
V E E E E E E E E M M M M M M M M M M M M M M M M M M M M M M M
Exponent Mantisse
Sign
The representation of a floating-point number (-1)
VZ
· m · 2 e comprises:
ƒ VZ = sign (0 – positive, 1 – negative)
ƒ e = exponent (e = exp - 127)
ƒ m = mantisse (m = 1.M ; 1 <= m < 2)
The sign, exponent (exp) and the decimal point (M) of the number are saved in a floating-point number. They still have to be determined.
The following schematic shows how all of the three components are selected. In this case the maximum frequency is considered (50.0Hz float: 4248 0000 hex
⇒
50.0 dec)
4 2 4 8 0 0 0 0
Bit
31 24 23 16 15 8 7 0
0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 4 9 0
84 hex
= 132 dec
1/16 1/16
2
Exponent (Exp)
Sign (VZ)
Mantisse (M) – decimal place in the hex system
The number comprises the following elements:
(-1)
VZ
·1.M·2
Exp-127
= (-1)
0
·(1 + 9·(1/16) + 0·(1/16
2
))·2
132-127
= 1·1.5625·2
5
= 50.0

2. Converting floating-point numbers from the decimal into the hex format
The decimal number must be represented in the form (-1)
VZ
· 1.M · 2
Exp - 127
.
Let's consider this conversion using an example.
The maximum frequency (P1082) should, e.g. be set to 87.0Hz; to do this the following conversion is required:
•
Sign "+"
⇒
87=(-1)
0
·87
•
Which power of 2 fits in the number so that the rest results in a "one (decimal) point something"?
2
6
= 64
⇒
87 = 64 · (87/64) =
•
Subtract 1 according to the definition
= 2
6
· (1 + 87/64 – 1) =
= 2
6
· (1 + (87/64 – 64/64)) =
•
Represent 6 as 133-127 according to the definition
= 2
133-127
· (1 + 23/64) =
•
The value 23/64 must be represented as a multiple of 1/16, 1/256 etc.
= 2
133-127
· (1 + 92/256) =
= 2
133-127
· (1 + (80+12)/256) =
= 2
133-127
· (1 + 5/16 + 12/256)
⇒
⇒
VZ = 0,
Exp = 133 dec
= 85 hex,
Mantisse = 5.12
dec
Mantisse (M)
0 8 5 5 12
0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0
…
E
Send via Profibus: 42AE 0000.
0 0 0