Sorry :) The idea that neurons are binary and just "on/off" units is a very antiquated way of looking at them. Certainly an action potential- the method of neurotransmission- is itself rather binary, but that alone is not the whole story. This is because neuronal membrane potentials are very important in establishing the functional state of a cell. The membrane potential is generally the difference in electrical potential between outside and inside the cell, expressed in mV's. At rest, neurons enjoy a resting membrane potential at around -70mV. However many neurons have oscillating membrane potentials that influence how they will respond to incoming signals. Simply put, when a neuron receives exitatory input (can be from 10,000 synapses on its dendrites), they cause shortly lived depolarizations, called excitatory post-synaptic potentials (EPSPs). As they all flow down the dendrites into the cell body, they interact, and if the resting potential depolarizes to around -55mV or so, we see an action potential. Now there are all sorts of exceptions and complex issues Ive purposely overlooked, but this is generally the main concept in our ideal neuron. So if we have an oscillating resting potential, and those EPSPs arrive when the oscillation causes a more depolarized resting state, we have a greater chance of causing an action potential. This is one way how the neuron dynamically gates information it receives and determines whether this is salient enough to pass onto its tens of thousands of neighbors.

So it's a little more complex than on or off. Neurons are very dynamic and do not passively receive information. :)