I have been thinking about how to think in binary notation. I know that decimal notation is just one way to represent numbers. Yet the decimal notation is so ingrained into my concept of numbers, that it is hard to see, that it is only representation. If I look at a binary number, I need to convert it to decimal to understand it. I know it is an unnecessary step.
I would like like to be able to think in both binary and decimal systems (and I also plan to be able to think in other numeral systems).
I do not have an exact reason for why I want to be able to do this. I feel that it would allow me to appreciate and understand math more closely and maybe to get a feel for the underlying structure of the number systems, which I do not possess at the moment. I also have a feeling that it might be useful for kids to be able to think in multiple numeral systems. I want to try it with my own kids. I suspect it will deepen the intuitive understanding of orders of magnitude and it may even help with spoken language learning. I could elaborate more, but I suspect, this is not the place.
I feel numeral languages are similar to spoken languages - some ideas are more easily expresses in English, but others are more easily expressed in Japanese.
The question - is there a "language" on how to think in binary? Let me explain. I do not want to use ones and zeros, because it is hard for me, not to see a decimal number in it. And I want to be able to read it and have a grammar for orders of magnitude. You would usually read binary number 1001 (9 in base 10) as one-zero-zero-one, but it is hard to understand. I would like something similar to the decimal system. You say twenty-two thousand, four hundred sixty-seven, not two-two-four-six-seven. I have come up with my own binary language, but I wonder if there is already some standard way. So I'm not reinventing the wheel. I don't know where to look or how to write a query for it. And a second question. If there is no standard binary language, is there someplace on the internet where I could discuss and share my language?
In case you wonder how this language looks like, there are a few examples:
\begin{array} {|r|r|r|r|} \hline Classical\ binary\ notation &Decimal\ notation&New\ binary\ notation &Pronunciation \\ \hline 0 &0& Ɔ&ba \\ \hline 1 &1& ſ&ta \\ \hline 10 &2& ſƆ&tajba \\ \hline 11 &3& ſſ&tajta \\ \hline 100 &4& ſƆƆ&tambajba \\ \hline 1011 &11& ſƆſſ&rata\ bamtajta \\ \hline 10000 &16& ſƆƆƆƆ&ratajba \\ \hline 10001 &17& ſƆƆƆſ&ratajba\ bambajta \\ \hline 101010 &42& ſƆſƆſƆ& ratambajta\ bamtajba\\ \hline \end{array}