Why should a number be separated from its base-10 representation?

"Before we do anything with bases, let’s talk about the concept of number, generally. The question “what is a number?” sounds like the dumbest question I could possibly ask you. Yet I predict that unless you’ve studied this material before, you have a whole bunch of tangled thoughts in your head regarding what “numbers” are, and those tangled thoughts are of two kinds. Some of them are about numbers per se. Others are about base-10 numbers. If you’re like most people, you think of these two sets of concepts as equally “primary,” to the point where a number seems to be a base-10 number. It’s hard to conceive of it in any other way. It’s this prejudice that I want to expose and root out at the beginning. Most people, if I asked them to name a number, would come up with something like “seventeen.” This much is correct. But if I asked them what their mental image was of the number “seventeen,” they would immediately form the following unalterable picture: 17 To them, the number “seventeen” is intrinsically a two-character-long entity: the digit 1 followed by the digit 7. That is the number. If I were to tell them that there are other, equally valid ways of representing the number seventeen — using more, less, or the same number of digits — they’d be very confused. Yet this is in fact the case. And the only reason that the particular two-digit image “17” is so baked into our brains is that we were hard-wired from an early age to think in decimal numbers. We cranked through our times tables and did all our carrying and borrowing in base 10, and in the process we built up an incredible amount of inertia that is hard to overcome. A big part of your job this chapter will be to “unlearn” this dependence on decimal numbers, so that you can work with numbers in other bases, particularly those used in the design of computers."