# Decimal to Binary Conversion

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I'm posting this in the General Programming Forums, but it may really belong in the Math Forum...

While working on a project involving reading GIS data from a file, I somehow got myself side-tracked onto writing some functions that convert between the native floating points values to their binary IEEE754 equivalent (without taking the floating point variables pointer and casting it to a matching size integer pointer).

So I started researching the conversion process, and found this website with a procedure.

My code starts by separating the integral and fractional parts using the C/C++ modf function.

 /* * FloatType is a template param = Input Type * UnsignedIntegerType is a template param = Output Type * MantissaBitCount is a template param stating the number of bits to use to store the mantissa in the output * ExponentBitCount is a template param stating the number of bits to use to store the exponent in the output * FindMostSignificantBit is a function that returns the highest flagged significant bit in an integer. * * * MantissaPivot will eventually be translated to the exponent * * Unlike the example I am multiplying by 256 (instead of 2), allowing for 8 bits to be extracted after each iteration. */ const FloatType Zero(0); const FloatType One(1); const FloatType Factor(256); const UnsignedIntegerType FactorSize(8); int MantissaSize(-1); int MantissaPivot(-1); /* Used to test for infinity */ const bool GreaterThanZero(Input > Zero); /* Used to test for overflow */ const bool GreaterThanOne(Input > One); UnsignedIntegerType Mantissa(0); do { Mantissa <<= FactorSize; FloatType Integral; const FloatType Fractional(std::modf(Input, &Integral)); /* This fails with large Integrals */ const UnsignedIntegerType ToMantissa(static_cast<UnsignedIntegerType>(Integral)); if(MantissaSize == -1) { if((ToMantissa == 0) && (GreaterThanOne == true)) { /* Number was too large to cast to an int */ } /* Initial Length */ const int MostSignificantBit(FindMostSignificantBit(ToMantissa)); MantissaSize = MostSignificantBit; /* Number of bits before most significant bit */ MantissaPivot = (MostSignificantBit > 0) ? (MostSignificantBit - 1) : 0; } else { /* I don't know what to call this other than non-initial */ if((Mantissa == 0) && (ToMantissa != 0)) { const int MostSignificantBit(FindMostSignificantBit(ToMantissa)); /* * Number of bits before most significant bit * At this point, we are dealing with the decmal and a negative * number. The means we start counting from the highest possible * bit count the number of bits between it and the most siginifcant * bit, including the most signficant bit itself. */ MantissaPivot -= (static_cast<int>(FactorSize) - MostSignificantBit + 1); /* * Don't count the leading 0's, since there was no significant values * stored in the mantissa yet. */ MantissaSize += MostSignificantBit; } else { if(Mantissa == 0) { MantissaPivot -= FactorSize; } else { MantissaSize += FactorSize; } } } Mantissa |= ToMantissa; Input = Fractional * Factor; } while((MantissaSize < MantissaBitCount) && (Input > Zero)); // More code follows for constructing the binary after it has been parsed into the mantissa and exponent 

As on the example website, I try taking the Integral part and convert it to a native integer. The problem I'm having is if Integral part of the float is larger than what can be stored in a the output integer. Casting to a larger type is not really an option, since the code supports doubles and 64-bit integers. Any ideas on how to convert these large values into a usable mantissa and exponent without using an non-standard cheats?

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