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In a discussion we're having on our compsci forums at uni, about binary numbers, someone brought up the notion of non-integral bases. I take it to mean numbers with bases that aren't integers. Is this right?

I've never encountered such a thing before, so I'm curious about it. I've only seen bases defined as integers - is it valid to think of non-integral bases? Do the same processes for understanding and converting integer bases apply to non-integers?

I have no specific questions, really. How does it work? How is it meaningful? What are some applications of it? Links to further information would be nice.

Searching the web turns up almost no information about this, so I wonder if it goes by any other names too.

Thanks to anyone who can shed some light on the matter.