No, you cannot map every particle. It violates the uncertainty principle, as well as requiring the same number of particles to represent the bits. Entropy probably has something to say about it too.
Ok I just had a cool thought on my idea of thinking only in terms of distance.
Forget about temperature, velocity, mass, gravity and momentum for a moment. Think only in terms of distance in space and the movement of particles. And assume this space can vary in density.
Now think of distance as a potential route for a particle to travel in space. It's an option, a probability. "Mr. Quark, you can move this distance or you can say still, which will it be?".
If completely uncompressed empty space has zero distance, what I am really saying is it has zero probability for movement. It has no 1s or 0s. A particle cannot move in this space, therefore the matter has no temperature, no gravity, no energy and no mass. It almost doesn't exist.
Now think of the space compressing and becoming denser. What is really happening is the number of probabilities of movement is increasing. There are now some 1s and 0s and the particle has freedom to move over distance (but not much).
Now imagine even denser space where particles have great freedom to vibrate and move over distance. But instead of distance think of probabilities.
Could it be that matter has some instinct to move and is attracted to "denser space", and that is what gravity really is? Just clumps of matter in compressed space with room to breath so to speak? So going by this logic if you can call it that, reality can be simplified in to nothing but varying densities of space and in that space are degrees of freedom dictated by probabilities... which are nothing more than binary code. And if you just flipped the code to the opposite values you get anti-matter.
Maybe there is a finite number of bits in the universe and they have to be rationed out, and form these denser clumps and eventually patterns and life.