The simplest would be to take each digit and treat it as a bit. Each group of 8 bits can be stored in a byte. Then you can send it as a stream of bytes. You will also need to store the length of the original string so that you can distinguish between "0" and "00".
Here is one way you could write the conversion from string to a byte array:
byte[] convertToBytes(string s)
{
byte[] result = new byte[(s.Length + 7) / 8];
int i = 0;
int j = 0;
foreach (char c in s)
{
result[i] <<= 1;
if (c == '1')
result[i] |= 1;
j++;
if (j == 8)
{
i++;
j = 0;
}
}
return result;
}
Reversing the operation is very similar.
If you need to transmit the data as a string you can base 64 encode the resulting byte array.
You may also want to consider keeping it in this form in memory too. This will be much more efficient than storing it as a string where each digit is stored as a 2 byte character. You are using roughly 16 times more memory than you need to for storing your data. The disadvtange is that it is slightly more difficult to use in this form, so if you have enough memory then what you are currently doing might be just fine.