Technically, yes. Computer memory works by storing electrons: if a memory bit has electrons, then it’s a 1; and if it has no electrons, then it’s a 0. [Electrons have mass](https://en.wikipedia.org/wiki/Electron_mass), and so every bit that’s flipped to 1 by storing electrons will add mass to the memory. However, we’re talking *minuscule* amount of mass, 9.109 x 10^-31 kg per electron, which is so small that even with several billion electrons stored, a human would not be able to tell a difference by picking up the full memory, and it would take an extraordinarily precise scale to detect the difference in weight.
So, technically yes, but for practical purposes, no.
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