I wonder what you are really trying to do, once you get the answer to this question. Where is your "huge decimal number" really coming from?

If you are just playing with powers 1024, it might be good enough to know that the binary representation for 1024 is a "1" followed by 10 zeros. That is:

$binary_string = "1" . "0" x 10;
print "$binary_string\n"
[download]

For each power of 1024, just add ten more zeros:

$power = 4;
$binary_string = "1" . "0" x (10 * $power);  # parens required
print "$binary_string\n"
[download]

But I assume you are really trying to do something more complicated than that. For example, if you are trying to read a string of decimal digits of arbitrary length, and convert that to binary, I'm not sure anyone has posted a good solution for that yet. (I don't have a good solution for that, but I'm sure one can be found...)