Basically, it costs free energy to forget a bit. If you flip a bit, that doesn't mean you forget it, as long as you remember you'll have to flip it back (or reinterpret it).
("Basically" because there are whole books on the subtleties of physics and information. I haven't mastered them.)
This is the correct answer. If you don't overwrite a bit, but instead move the old value to an auxiliary bit known to be zero, that can be theoretically done for free.
("Basically" because there are whole books on the subtleties of physics and information. I haven't mastered them.)