I know, the question sounds very stupid when you first read it. But my thinking is this: As I understand it, most (all?) memory or storage technologies use cells that can have two distinct levels of energy. The energetically higher one (a charged capacitor in RAM; magnetisation in a hard drive or floppy disk; a charged oxide in flash memory) corresponds to a 1, its opposite to a 0. In line with E = mc², that would mean that the cell with a 1 in it would have to have a greater total mass, right? Very, very slightly, but still. Or perhaps the effect isn’t even so slight at the tiny molecular levels modern memory technology operates at?
This was discussed in the thread linked below.
Some memory devices do use energy levels, and yes, in such a case, one of them will be ever-so-slightly more massive than the other (though so small you’d never be able to detect it). But I don’t think it’s a given that the 1 is always higher energy than the 0, and there are ways to store a bit that have the same energy for both.