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How does MLC FLASH store multiple bits per cell? I understand that each cell is one MOSFET, are the different bits represented by multiple voltage levels (as opposed to just high/low, which would then be SLC)?

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Yes, so an MLC flash chip that stores 4 bits per cell would have 16 different charge states. In general \$2^n\$ charge states for \$n\$ bits. A modern 8TB QLC drive might have 8 dies of 1Tb each.

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