Endress+Hauser EngyVolt RV12, Руководство по эксплуатации

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Appendix EngyVolt RV12
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mantissa is always arranged to be 1 and is thus not needed in the representation of the
number. The process by which the most significant bit is arranged to be 1 is called
normalisation, the mantissa is thus referred to as a “normal mantissa”. During
normalisation the bits in the mantissa are shifted to the left whilst the exponent is
decremented until the most significant bit of the mantissa is one. In the special case where
the number is zero both mantissa and exponent are zero. The bits in an IEEE 754 format
have the following significance:
Data Hi Reg, Hi Byte. Data Hi Reg, Lo Byte. Data Lo Reg, Hi Byte. Data Lo Reg, Lo Byte.
SEEE
EEEE EMMM
MMMM MMMM
MMMM MMMM
MMMM
Where:
S = represents the sign bit where 1 is negative and 0 is positive
E = is the 8-bit exponent with an offset of 127 i.e. an exponent of zero is represented by
127, an exponent of 1 by 128 etc.
M = the 23-bit normal mantissa. The 24th bit is always 1 and, therefore, is not stored.
Using the above format the floating point number 240.5 is represented as 43708000 hex:
Data Hi Reg, Hi Byte. Data Hi Reg, Lo Byte. Data Lo Reg, Hi Byte. Data Lo Reg, Lo Byte.
43 70 80 00
The following example demonstrates how to convert IEEE 754 floating-point numbers
from their hexadecimal form to decimal form. For this example, we will use the value for
240.5240.5 shown above.
The floating-point storage representation is not an intuitive format. To convert this
value to decimal, the bits should be separated as specified in the floating-point
number storage format table shown above.
For example:
Data Hi Reg, Hi Byte. Data Hi Reg, Lo Byte. Data Lo Reg, Hi Byte. Data Lo Reg, Lo Byte.
0100→0011 0111→0000 1000→0000 0000→0000
From this you can determine the following information.
• The sign bit is 0, indicating a positive number.
• • The exponent value is 10000110 binary or 134 decimal. Subtracting 127 from 134
leaves 7, which is the actual exponent.
• • The mantissa appears as the binary number 11100001000000000000000
There is an implied binary point at the left of the mantissa that is always preceded by a 1.
This bit is not stored in the hexadecimal representation of the floating-point number.
Adding 1 and the binary point to the beginning of the mantissa gives the following:
1.11100001000000000000000
Now, we adjust the mantissa for the exponent. A negative exponent moves the binary
point to the left. A positive exponent moves the binary point to the right. Because the
exponent is 7, the mantissa is adjusted as follows: 11110000.1000000000000000.
Finally, we have a binary floating-point number.
Binary bits that are to the left of the binary point represent the power of two
corresponding to their position. The result is the following decimal value:
.11110000 = (1 x 2
7 ) + (1 x 2 6 ) + (1 x 2 5 ) + (1 x 2 4 ) + (0 x 2 3 )+ (0 x 2 2 ) + (0 x 2 1 )+ (0 x
2 0 ) = 240