This is too speculative to give a scientific answer, however based on some pretty dreamy considerations, Hans Moravec, a famous "trans humananist" has suggested that human memory requires 100 million megabytes of storage. This was worked out by estimating the number of total synapses in the human brain. First of all nobody knows for sure what this number is. Second it ignores the many other mysterious processes that go on in the brain that do not involve nerves (e.g. glial cells) as well as more complex interactions between neurons and brain chemicals that are currently not known. The fact is nobody knows the answer to your question. Not at all. However, if you are writing science fiction and you want a number, say 100 million megabytes. (Personally I think this is way too low.) For a good paper on this (but remember it's very speculative and not based on very much science) check out Hans Moravec's 1997 paper "When will computer hardware match the human brain?"
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