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138 SPSx51 Modular GPS Receivers User Guide
• Sign bit field
The sign bit field is the most significant bit of the floating-point number. The
sign bit is 0 for positive numbers and 1 for negative numbers.
• Fraction field
The fraction field contains the fractional part of a normalized number.
Normalized numbers are greater than or equal to 1 and less than 2. Since all
normalized numbers are of the form 1.XXXXXXXX, the 1 becomes implicit and
is not stored in memory. The bits in the fraction field are the bits to the right of
the binary point, and they represent negative powers of 2.
For example:
0.011 (binary) = 2-2 + 2-3 = 0.25 + 0.125 = 0.375
• Exponent field
The exponent field contains a biased exponent; that is, a constant bias is
subtracted from the number in the exponent field to yield the actual exponent.
(The bias makes negative exponents possible.)
If both the exponent field and the fraction field are zero, the floating-point
number is zero.
• NaN
A NaN (Not a Number) is a special value which is used when the result of an
operation is undefined. For example, adding positive infinity to negative infinity
results in a NaN.
FLOAT data type
The
FLOAT data type is stored in the IEEE single-precision format which is 32 bits long.
The most significant bit is the sign bit, the next 8 most significant bits are the exponent
field, and the remaining 23 bits are the fraction field. The bias of the exponent is 127.
The range of single-precision format values is from 1.18 x 10
–38
to 3.4 x 10
38
. The
floating-point number is precise to 6 decimal digits.
0 000 0000 0 000 0000 0000 0000 0000 0000 = 0.0
0 011 1111 1 000 0000 0000 0000 0000 0000 = 1.0
1 011 1111 1 011 0000 0000 0000 0000 0000 = -1.375
1 111 1111 1 111 1111 1111 1111 1111 1111 = NaN
S
Exp. + Bias
Fraction
31 30 23 22 0