Can the human brain be reduced to a binary system?
First of all, I would like to point out that making analogy between digital computers and the brain is often very misleading.

That being said, my answer is, some scientists believe so, some don't.

Several things to consider:


Some neural systems are not spiking. C. elegans for example has a nervous system that is entirely analogue. Human nervous system also contains neurons with graded responses (mostly in the sensory front-end though).
Spiking neurons may be binary at each time point, but time itself is continuous. Firing at 0.003 seconds later can represent something different. (in contrast to the usual synchronous digital architecture of computers)
The neuron doctrine is sometimes challenged. Glial cells that do not fire may have important functions for information processing. See:


Bullock, T. H., Bennett, M. V. L., Johnston, D., Josephson, R., Marder, E., and Fields, R. D. (2005). The neuron doctrine, redux. Science, 310(5749):791-793.