Trimble R10 - FLOATING-POINT data types

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Floating‐PointNumber=<sign>1.<fractionfield>x2(<ex ponentfield>‐bias)
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that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
1038.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
DOUBLE
TheDOUBLEdatatypeisstoredintheIEEEdouble‐precisionformatwhichis64bitslong.Themost
significantbitisthesignbit,thenext11mostsignificantbitsaretheexponentfield,andthe
remaining52bitsare
thefractionalfield.Thebiasoftheexponentis1023.Therangeofsingle
precisionformatvaluesisfrom2.23×10–308to1.8×10308.Thefloating‐pointnumberisprecise
to15decimaldigits.
