Think languages. In English an accordion is called an accordion. In French it's un accordéon, in Russian аккордеон, and in Klingon may'ron, but the thing itself is the same no matter what you call it. (Okay, maybe not exactly the same among the Klingons, but it looks pretty similar.)
The idea behind numbers in different bases is the same: it's still the same number, just written a little differently.
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