SRAM, DRAM, Flash, EPROM - all of the memory cells contain one bit of data each. Is there any memory cell that can store more than one bit, e.g. 2 bits/4bits?
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Yes. When you get down to the level of a memory cell, the circuitry is pretty analog. So you can store multiple voltage levels in the cell, and interpret those multiple levels as encoding more than one bit.
There are parts in production that use this.
Google "multi-level memory".
Actually you’ll have a really hard time to find a NAND flash device that does not store more than one bit per cell nowadays. This is one of the reasons the price of memory cards and SSDs (in terms of $/GB) has dropped so dramatically over the years.
Of the semiconductor memories on the market, only some Flash EPROM technologies store more than 1 data bit per memory cell.
As an example, the Cypress Mirrorbit technology stores two data bit in a single Flash memory element, utilising four stored voltages to do so. You'll find details of those parts on the internet.