Oh boy, I am not sure I have the vocabulary to explain this effectively. But I will try!
Okay so normally when we say “base 10” or “base 2”, the number in that description is itself in base 10, right? Like the “10” in “base 10” means the number of fingers most humans have (including thumbs), and the “2” in “base 2” means the number of things in a pair.
You will note, though, that for that “10” to mean what it means, and that “2” to mean what it means, they must be in base 10 themselves. A pair of things in base 2 is 10 things, right? So then if you write the “2” in “base 2” in base 2, it’s “base 10”. And this holds true for any base. How do you write a dozen in base 12? 10. So base 12, written in base 12, is base 10.
Oh boy, I am not sure I have the vocabulary to explain this effectively. But I will try!
Okay so normally when we say “base 10” or “base 2”, the number in that description is itself in base 10, right? Like the “10” in “base 10” means the number of fingers most humans have (including thumbs), and the “2” in “base 2” means the number of things in a pair.
You will note, though, that for that “10” to mean what it means, and that “2” to mean what it means, they must be in base 10 themselves. A pair of things in base 2 is 10 things, right? So then if you write the “2” in “base 2” in base 2, it’s “base 10”. And this holds true for any base. How do you write a dozen in base 12? 10. So base 12, written in base 12, is base 10.
Nailed it. This was a perfect explanation. Thank you!
There is an old unix calculator program called bc where one can change the input and output base.
If you change the input base and then the output base strange things happen as bc interprets the output base number in the input base .
ibase=2 obase=10 The output base is now 2 (in base 10)