10^11 neurons, 10^4 synapes per neuron - even if each synapse can be represented as a single 8 bit number (very optimistic), that's a petabyte of storage needed. Bostrom puts a hundred terabytes as the lowest estimate, with spiking neural network at 10 petabytes. Metabolism being required too would push the estimate to an exabyte, and the more pessimistic (but less plausible models) go beyond this.

And yes, an AI might be more efficient than the brain, but if its being created by evolution then I don't think it espeically likley that it will be more efficient than brains created by evolution.