Write real binary to file - c++

Question

I am currently working on a project to read binary data from a file do stuff with it and to write it back again. The reading works well so far, but when I try to write the binary-data stored in a string to a file, it writes the binarys as text. I think it has soemthing to do with the opening mode.
Here is my code:
void WriteBinary(const string& path, const string& binary)
{
ofstream file;
file.open(path);
std::string copy = binary;
while (copy.size() >= 8)
{
//Write byte to file
file.write(binary.substr(0, 8).c_str(), 8);
copy.replace(0, 8, "");
}
file.close();
}
In the function above the binary parameter looks like this: 0100100001100101011011000110110001101111

Answer 1

With the help of "aschelper" I was able to create a solution for this problem. I converted the binary string to its usual representation, before writing it to the file. My code is below:
// binary is a string of 0s and 1s. it will be converted to a usual string before writing it into the file.
void WriteBinary(const string& path, const string& binary)
{
ofstream file;
file.open(path);
string copy = binary;
while (copy.size() >= 8)
{
char realChar = ByteToChar(copy.substr(0, 8).c_str());
file.write(&realChar, 1);
copy.replace(0, 8, "");
}
file.close();
}
// Convert a binary string to a usual string
string BinaryToString(const string& binary)
{
stringstream sstream(binary);
string output;
while (sstream.good())
{
bitset<8> bits;
sstream >> bits;
char c = char(bits.to_ulong());
output += c;
}
return output;
}
// convert a byte to a character
char ByteToChar(const char* str) {
char parsed = 0;
for (int i = 0; i < 8; i++) {
if (str[i] == '1') {
parsed |= 1 << (7 - i);
}
}
return parsed;
}