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Many microprocessors have a specified lower limit on clock frequency (apart from the maximum clock frequency limit) because ?
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Clcok frequency becomes low means time period of clock becomes high. When this time period increses beyond the time period in which the non-volatile memory contents must be refreshed, we loose those contents. So, clock frequence can't go below this value.

The cache, register etc. inside CPU and RAM for primary memory are all examples of volatile memory and needs refresh within the specified time period or else will loose their contents.

Non-volatile memory are being developed and computers in future should be tailor made for that.
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@Arjun Why you said cache, register and RAM comes under non volatile memory?
Sorry, it was a typo. Thanks..

non-volatile memory contents must be refreshed.  I think it should also be volatile.

do contents get lost in volatile memory even if there's no power failure?


Yes. RAM has to be refreshed periodically. Source: Wiki

Memory refresh is the process of periodically reading information from an area of computer memory and immediately rewriting the read information to the same area without modification, for the purpose of preserving the information.[1]

In a DRAM chip, each bit of memory data is stored as the presence or absence of an electric charge on a small capacitor on the chip.[2][3] As time passes, the charges in the memory cells leak away, so without being refreshed the stored data would eventually be lost.

For example, the current generation of chips (DDR SDRAM) has a refresh time of 64 ms and 8,192 rows, so the refresh cycle interval is 7.8 μs.[5][9]

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