## How to detect if a base 10 decimal can be represented exactly in base 2

As part of a numerical library test I need to choose base 10 decimal numbers that can be represented exactly in base 2. How do you detect in C++ if a base 10 decimal number can be represented exactly in base 2?

My first guess is as follows:

``````bool canBeRepresentedInBase2(const double &pNumberInBase10)
{
//check if a number in base 10 can be represented exactly in base 2
//reference: http://en.wikipedia.org/wiki/Binary_numeral_system
bool funcResult = false;

int nbOfDoublings = 16*3;
double doubledNumber = pNumberInBase10;
for (int i = 0; i < nbOfDoublings ; i++)
{
doubledNumber = 2*doubledNumber;
double intPart;
double fracPart = modf(doubledNumber/2, &intPart);
if (fracPart == 0) //number can be represented exactly in base 2
{
funcResult = true;
break;
}
}
return funcResult;
}
``````

I tested this function with the following values: -1.0/4.0, 0.0, 0.1, 0.2, 0.205, 1.0/3.0, 7.0/8.0, 1.0, 256.0/255.0, 1.02, 99.005. It returns true for -1.0/4.0, 0.0, 7.0/8.0, 1.0, 99.005 which is correct.

Any better ideas?

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What resources are out there and what is a good starting project?