The interesting thing here is, what V1 does is it computes directional receptive fields based on raw data from the retinas. We can implement that in a tiny silicon chip, maybe even just a DSP chip, not a full CPU. We know how to implement this kind of computation super efficiently, and without using neural networks.
We don't fully understand what goes on in many areas of the brain, but if we can find efficient ways to implement equivalent computations, we might technically already have sufficient manufacturing technology to implement equivalent functionality in a pretty compact and power-efficient form factor, or we might not be that far from there.
A classic quote from Dijkstra: "The question of whether machines can think is about as relevant as the question of whether submarines can swim."
If there were a brain region that might be emulated to reproduce "general information processing", the best candidate would probably be neocortex. As far as I am aware, that does seem to be a very wide region of the brain which has fairly consistent structure, and largely serves to integrate all other systems.
The point is that V1 is a large part of the visual cortex. It's something the brain dedicates a lot of resources to, and we could implement something similar in silicon almost trivially. Your smartphone GPU may have enough compute to simulate an equivalent computation at 200 frames per second.
It's possible that in the future, we'll be able to simulate consciousness very efficiently once we have a better handle on the kinds of computations that are involved, much more efficiently than what the brain does.
But even in this noisy environment, our brains can usually operate just fine. Given this level of background noise, I would be very surprised if the average synapse would require more than a 16-bit floating point value for its outputs.
Some synapses contain multiple receptor sub-types. Dopamine, for example, has some receptors which are inhibitory, and others which are excitatory. Each receptor is sensitive to different concentrations of dopamine. This gives the effect that when the dopamine concentrations in the synapse are low, this synapse acts to inhibit the activity of the efferent neuron, while when the concentration reaches a certain threshold, the output of the synapse flips to an excitatory signal.
How would you model that system with a single F16?
And that's just one example: for instance there are specific signals which trigger cascading effects in the neuron which up-regulate certain chemical pathways, causing an amplifying effect on other signals.
Or you have shunting effects, where an inhibitory synapse placed at a certain point in the dendritic arbor serves to selectively cancel signals from farther down that one specific branch of the dendrite.
That's not "noise" - the brain has incredibly refined and detailed mechanisms for information processing which go very far beyond `weight * sigmoid(activation) = output`