That's a weird non-joke version. The ones I know are:

The usual:

    There are 10 kinds of people in the world, those
        that understand binary and those that don't.

Then there was:

    There are 11 kinds of people in the world, those
        that understand binary and those that don't.

Which is a riff on:

    There are 3 kinds of people in the world, those
        who can count, and those who can't.

Then along came:

    There are 10 kinds of people in the world, those
        that understand binary, those that don't, and
        those that didn't expect this joke to be in
        ternary.

Yours, on the other hand, just doesn't really make sense. Maybe I'm missing something ...

There are 10 kinds of people in the world. Those who understand binary, those who don't, and those who didn't expect this to be in base 3.

I always hated this joke because to me understanding binary does not mean understanding two's complement. Thus the joke took a on a meta-joke: using two bits to represent a binary state instead of one bit. If the joke teller understood binary in their heart they would use a proper enumeration without just using integers.

Also the proper syntax is 0b10 not 10.

There are 10 kinds of people in the world. The ones who understand binary and 9 others I can't remember.

Binary, as easy as 1, 10, 11.