Just connecting these drives isn't going to tax the RAM that much; it really depends on what you do with them more than anything. 4 GB RAM is a bit minimal these days, and RAM's not that expensive, so I'd up it to 8 GB just for good measure. If you don't have enough USB ports, you can get expansion cards to give you more.
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Good luck.
I have a Acer computer doing nothing but gathering dust and I have 7 hard drives. I have 2 hard drive covers and 2 2 place hard drive docking stations. I want to hook all these to the Acer, with 4 gig of RAM. I forget in all that I have learned on here if I can do this or if I need more RAM or just forget it. Thanks

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