If a quick format just marks bits as writable, and a normal format writes 0s to the entire disk, why do people bother with DBAN, and why are multiple passes ever required?
It used to be possible by reading the residual magnetism left by the previous bit. This isn't so much of an issue now that the tracks and bits that hard drives write are so small. It is almost impossible to recover any meaningful data off of a zeroed drive with modern disks.
EDIT: This next section is only true for XP. Psycogeek pointed out that Vista and up does zero out the drive if you do a full format.
That being said, your definition of quick format and normal format is off. A normal format doesn't zero out the disk, that would take too long. The difference between the two is that the normal format looks for bad sectors on a drive, while the quick does not.
So it's best to use a tool like DBAN to at least do one pass if you want to make sure data isn't recoverable. And if you're doing one, why not a few more for fun!