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Q.1 A 32 bit wide main memory unit with a capacity of 4GB is built using 128M *8 bit DRAM .the number of rows of memory cells in the DRAM chip is $2^{12}$ and time require to refresh operation is 20 nsec.total amount of time require to refresh the 4GB DRAM is………..?

Ans-81.92 microsec.

explanation ????
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Let's say there are x DRAM chips, each with 2^12 rows and refresh operation takes 20nsec.

So to perform refresh on 1 DRAM chip it would take 2^12*20 nsec = 81.92usec and one more thing to notice here is that the refresh operation for one row on all chips can be performed simultaneously..

Refresh operation on first row of all chips can be done in 20usec[0-20] and on second row of all chips can be done 20sec[20-40] and so on..
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ANS :81.92 microsecond

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now, at a time one refresh operation take one row which means

in this we have 2^12 rows

so 1 refresh operation = 1 row ->20ns

so 2^12 rows=20ns * 2 ^12 =81.96micro second

extra info:

why refresh needed in dram ??

dram stores the capacitor to store the charge as data as there is capacitor so possibilty of lossing the charges will occur hence to avoid data loss we need refresh