There are at least three phenomena, which may play the role:
A too short information can easily interfere. So if it is on/off, it may interfere with its state a few days before, or with if the iron is on or off.
Moreover, things are remembered with redundancy. So, for example, one can remember not only PIN as numbers visually, but also as words, as a 'snapshot' of numbers written on a letter, as a sequence of finger moves, etc. So in case one is lost or inactive, all other can be used instead.
Also, one there is a piece of information, you can relate (consciously or not) to other objects. E.g. you can additionally remember that there are two digits from your birthdate and there is 8, a number you like very much, ...
Actually, mnemonic techniques base on the three observations, to make it easier to learn or harder to forget.
As a side note, computational analogues (esp. number of bits) are usually very misleading when it comes to human mind. The later does not work as an easy in/out device storying faithfully digital information.
(BTW: very likely, still it is much easier to remember 4 digits (of base 10) than 14 zeroes/ones.)