Knowing there are 100,000,000,000 neurons in an average human brain, and 7,000 dendrites in each neuron, and neurons are connected to each other by dendrites and axon terminals, how many synapses are there in an average human brain? (I don't know how many axon terminals per neuron there are on average.)
The human neocortex contains approximately 1.5x10^14 synapses, connecting its 19–23 billion neurons.
Source: Pakkenberg, B., Pelvig, D., Marner, L., Bundgaard, M. J., Gundersen, H. J. G., Nyengaard, J. R., & Regeur, L. (2003). Aging and the human neocortex. Experimental Gerontology, 38(1-2), 95-99. doi:10.1016/S0531-5565(02)00151-1
The neocortex is just sight and hearing. You really need to include the entire nervous system's number of nerves to truly appreciate the processing power of the human neural network. How many nerves are in the human body? Even an estimate of 10^11 (100 billion) neurons times an average of 7000 dendrites or 7.0 * 10^4 connections is 7.0 * 10^15 (7,000,000,000,000,000) or 7 quintillion neural connections. Each neuron operates once every 10 ms or 100 times per second, or 700 * 10^15 or 700 quintillion operations per second.
Furthermore, the chemical connection between neurons are effectively "analog", or floating-point, so the correct term isn't "bits per second" but FLOPS. Collectively, my estimate above based on common google searches is 700 exaFLOP per second. For comparison, new the supercomputer being installed at Argonne Labs operates at 1 exaFLOPS and comes with no software.