Somone has suggested that
Within, say, a collection of every possible 30 second long MP3 file encoded at 128kbps, I'd probably be infringing on a few thousand copyrighted works.
128kilobits per second = 128,000 bits per second * 30 seconds = 3,840,000 bits.
There are 2 to the 2,840,000 possible files of that length.
Ignoring the fact that most of those won't be valid mp3s, how can I quantify the amount of space needed to store all those files? For instance, is that more bits than there are atoms in the universe?
The total space is $2^{3,840,000}\cdot 3,840,000$ bits. This is a fine quantification, but if you want the number of zeros in base $10$, you can take the log of it. $$\log_{10}(2^{3,840,000}\cdot 3,840,000)=3,840,000 \log_{10} 2 + \log_{10} 3,840,000 \\ \approx 3,840,000\cdot 0.30103 + 6.58433 \approx 1,155,961$$
so you need a little more than a million zeros.