How inefficient! It only takes 10 distinct black-and-white pixels to represent 1000 distinct glyphs. Even low-res bitmap fonts are usually at least 6x6 pixels in size, meaning that we can use them to represent numbers in base 2^36. And with modern high-DPI screens we have easily enough room for glyphs that are 30 pixels square, letting us represent numbers in base 2^900. But why limit ourselves to black and white? We have the full 8-bit color space to work with, letting us devise a numeral system that can easily represent (2^24)^900 numbers using the space of a single glyph. :)
Base e would be the most efficient, if one assumes that the cost of representing a number in a particular radix is proportional to the radix. If you restrict the radix to natural numbers (e-state devices being rather hard to construct), base 3 would be more efficient.
As it happens, we've learned to make two-state devices way more cheaply than three-state devices, so binary wins in the real world, but if we figured out how to make three-state devices for at most 1.5 times the cost of two-state devices, base three would win.
It's fun to prove that base e and base 3 are theoretically more efficient than base 2 (and not all that difficult...only basic calculus is necessary).
