Yo!

* double XOR

>>8
^{DOUBLE XOR MY}_ANUS

Go back to /g/ please...

The question is not specific enough to have a real answer.
You would have to describe "the computer recognizes my password" in excrutiating detail.

/prog/ will be spammed continuously until further notice. we apologize for any inconvenience this may cause.

BIOS password? on the ROM
OS user passwprd? on the OS's user db.
Most OS use /etc/passwd
man passwd

>>1 not exactly, but kind of.
The main idea is a zero-knowledge-proof, (aka) a one-way-encryption, or cryptographic hash function. kind of like the examples #4-8 mentioned. (sort of)
So the idea is that it is easy to encrypt the password, say "password" gets turned to "0a976b832f...", but as difficult as possible to decrypt it back to what it was. And then an attacker will end up just having to try encrypting lots of possible passwords, and looking for one that matches the proof.
These aren't fool-proof, and there are ways to both 'crack' them (remote-style attacks, usually when you want to undo the encryption / recover the password) and/or wipe them (physical access/ boot into another OS and just wipe them out)