Imagine you write a '1' bit to a memory location - now you know for sure that the location contains '1' now, as you can check it anytime. But now you have absolutely no information about the past, either it was '1' before or '0'. So the number of legal states (and entropy) seemingly have decreased if you are considering this bit level macrostate. But according to the 2nd law the global entropy never decreases, so at least an equal entropy increase eventually should be there somewhere in the system (in the microstates - the states you did not considered as logically separate) - for example as a small heat increase.