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It's called base 16.
No, like I said, I mean actually leaving the standard digital system of writing numbers, if not completely than at least to some extent. See, the problem with binary is that, when you write it in 0s and 1s, it gets quite long to say even rather small numbers (like in the hundreds or thousands). To shorten it, we'd have to use different characters. But it seems to me that, so long as we use complex characters at all, binary is going to be too long. So instead, I've been thinking of new ways to write it, using simple characters. Dots and lines are one interesting possibility (turning '01001', for example, into '.|..|'), but can we get more efficient even than that?
What about the idea of, where there's a string of enough digits of the same type in a row, using a number inside brackets (or whatever) to represent it. So '0101100000000000010', instead of being '.|.||............|.', would be '.|.||<||..>|.'. See, I just got rid of six extra characters. Meanwhile, a computer would still remember it in binary and merely translate it to this system when displaying it on the screen. This is just one example of new ways in which we could write numbers to make it easier and more effective. Once you start thinking outside the box, there's tons of interesting stuff you can do.