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that's outside the scope. information storage is the point. 10,001 bytes storage available per cell. use generalization, of course... using information technology (modeling), not physics.
@ dugan- true, you dont need to use DIMMs. Though if I was designing a suercomputer I'd consider using standard DIMM sticks to save money.
2 minor additions to your maths-
You've used the stick only size, to be more accurate you probably should consider the extra size from mounting slots, and some extra room for airflow. You dont want your 4EB getting heat issues.
2GB DDR2 sticks, fair enough, but 8GB DDR3 sticks are easy to get. Being DDR3 the airflow requirements would be lower as well. If the 16 or 32GB sticks that samsung announced in 2009 are actually avaible, that would drop the required volume for 4EB a huge amount.
you left out address decoding that has a transistor count grater than that of the memory
IMO
a memory bank of this size would have to be built with flip chip mounting directly
to an 8 layer circuit board
because even in surface mount IC packages less than 10% of the volume is the chip it self
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