Single neurons don't store a variable. Not even close. Neurons have, on average, several thousand to several tens of thousands (depending on the brain region) of areas which receive signals (synapses). These areas receive signals from thousands (up to hundreds of thousands) of other neurons. Each synapse is composed of multiple active zones, each of which independently modulates the incoming signal. If enough of the active zones get activated strongly enough, the neuron sends the signal forward. Depending on how often signals come, and how strong they are, whether they result in a signal being sent onward, depending which neurotransmitters are used... each active zone can be changed, modulated in its responsiveness to the incoming signals. The ability to send the signal forward is also changed. The resulting effect is that a neuron is a qualitatively different thing to a variable; it is a microcircuit in itself, and with far,far more states than just 8 (where did you get that number?).
Next, your brains does not grow and fold depending on how you use it. Yes, a few hundred new neurons are made daily, probably (estimates vary wildly) - but they go to only two areas, the hippocampus (central coordinator of new memory formation) and the olfactory bulb (the part of the brain you use to detect scent). The vast majority of your brain is fixed after birth, and contains all neurons you will ever have; you can only lose them, never gain new ones. All folding is completed in infancy; you cannot grow more folds later in life.
What happens instead is that neurons rewire. The same cell can grow additional dendrites and axons (connections that receive or send signals, respectively). This can and does change the structure of the brain, making certain regions expand or contract by a bit (a very small bit, actually, except in extreme cases such as schizophrenia). But these are the same cells growing or pruning connections to other cells; you don't get entirely new elements in the ciruit. (Another reason why it is wrong to think of neurons as "variables;" each neuron is more like a very complex and constantly changing microcircuit on its own, even before you it connects to other neurons.)
I'm running out of time, so I'll skip over the central part which I'll call vaguely ok-ish, and go straight to the conclusion: no, consciousness is not software running on wetware.
All your perceptions get filtered through your unconscious brain. It forms associations, puts them in context, assigns them emotional valence (how important are they for you, do they deserve notice). It makes decisions, entirely without conscious input, as far as anyone has been able to show. It forms your thoughts (explanations of your thoughts and behaviors that fit into your personal and cultural worldview; this system probably evolved as a way to explain our behavior to others more than to actually reflect our real decision-making and thinking process). Then, all of this is dumped into your consciousness post hoc. Your conscious mind does not have a chance to influence anything; it has already happened, it is about 100-300 milliseconds too late.
Now, there is a part where you are almost correct. There is a completely subconscious level, which decides purely on heuristics, and which very quickly integrates an incredible amount of data. This is the level of the brain that allows you to catch a ball thrown at your face - imagine if you had to consciously calculate the trajectory, and decide where to put your hand before the ball reached you. This system provides you with most emotions, gut feelings or split-second impulses.
Then, there is the slow and very limited thinking process which appears to occur within the purview of consciousness. This is the level where you are thinking through the steps, and using your working memory, step by step. Figuring out a math problem you aren't familiar with works at this level. And most skill acquisition as well: driving starts at this level, then (as we gain experience) slowly sinks into the domain of instincts and learned automatic behaviors (we become able to lead a conversation or pay attention to other things while driving; we no longer have to consciously remember and pay attention to where exactly our hands and feet are, etc.). So far, this kind of fits the theory you have been building.
However, consciousness is actually kind of illusory even at this second level; "self" is constructed completely "in the past." Thinking and decision-making still happens before consciousness; decisions and thoughts get dumped into awareness after they have already formed (i.e. you become aware of what "you" are thinking or deciding after the thought has already been produced, and after the decision of how to move your body has already gone one to your muscles). The main difference between two processes is that in the second case, the steps through which the process goes also enter awareness - unlike the "fast" system, which only makes the (vague) product available, but keeps the steps and important factors completely beyond the conscious mind.
It is completely unknown (at least I haven't seen anything, and I follow the literature pretty religiously) why this process is connected to consciousness at all. There are many theories about it, but very little data. It could be simply that the second, evolutionarily newer system is cross-wired with the self-referencing neural networks which (most likely) allow the phenomenon of consciousness to exist. Who knows? FFS, we don't even have a workable definition of consciousness, much less a way of approaching the problem of its construction in any meaningful way. It is the last true complete mystery of neuroscience; for everything else, we have at least a set of decent basic ideas.
To finish up, let's go back to OP's original question. We actually don't have much trouble conceptualizing how abstractbehaviors occur. For instance, there is nothing particularly (conceptually) mysterious about a student solving a calculus equation - while the process is very different from what we see in a computer, the essential principle is that incoming sensations (reflections of the numbers and letters on a page as perceived by retinal cells) get filtered and shunted through tens of billions of steps into a set of behaviors (hand and arm movements) which produce a result (a solution written on that same pencil). While it would be difficult, a good engineer could today write a neural network simulation that would do the same thing (at least for a particular, narrow set of problems) - input a picture of a mathematical problem into a camera, and a robotic arm writes out the result. Practically difficult, but conceptually we are already there.