Преобразование целого числа в биты

I have byte to binary string function,

std::string byte_to_binary(unsigned char byte)
{
    int x = 128;
    std::ostringstream oss;
    oss << ((byte & 255) != 0);

    for (int i = 0; i < 7; i++, x/=2)
       oss << ((byte & x) != 0);

    return oss.str();
}

How can i write an int to bits in same way? I don't want extra 0's at the beginning of binary string so that is why i can't figure out how to create a variable length each time. Кроме того, я не использую std :: bitset.