The Represented Value - ashtech GG Surveyor Reference Manual

The Represented Value

The value of the number represented is equal to the exponent multiplied by the
fractional value, with the sign specified by the sign bit field.
If both the exponent field and the fraction field are equal to zero, the number being represented will
also be zero.
Note that in some systems (Intel-based PCs in particular) the order of the bytes will be reversed.
Single-Precision Float
The single precision format uses four consecutive bytes, with the 32 bits containing a
sign bit field, an 8-bit biased exponent field, and a 23-bit fraction field. The exponent
has a bias of 7F (hexadecimal). The fraction field is precise to 7 decimal digits. The
single-precision format can represent values in the range 1.18*10^-38 to 3.4*10^38
(decimal), as presented in Table D.1.
31-28
S EXPONENT
0000
0011
1111
0011
In Table D.1, the value 1.0 is calculated as shown below.
1.
2.
3.
4.
D-2
Table D.1: Single-Precision Format
27-24 23-20 19-16
FRACTION
0000 0000 0000
1111 1000 0000
1111 1111 1111
1111 0100 0000
The sign of the value is positive because the sign bit field is equal to 0.
The exponent field is equal to 7F (hexadecimal). The exponent is calculated
by subtracting the bias value (7F) from the exponent field value. The result
is 0.
7F - 7F = 0
The exponent multiplier is equal to 2^0, which is equal to 1 (decimal).
The fraction field is equal to .0. After adding the implicit normalized bit, the
fraction is equal to 1.0 (binary). The fraction value is equal to 2^0 (decimal),
which is equal to 1 (decimal).
The value of the number is positive 1*1= 1.0 (decimal).
15-12 11-8 7-4
0000 0000 0000
0000 0000 0000
1111 1111 1111
0000 0000 0000
GG Surveyor GPS+GLONASS Reference Manual
3-0
VALUE
0000 0.0
0000 1.0
1111 NAN
(not a number)
0000 0.75