# Radix

Radix (基數) forms the basic of number system. While radix basically mean how many numbers you can put into one digit. For a radix-R system $R \in {\mathbb Z}$, The the value of those numbers will be:

$$N = \sum^{n-1}_{m} a_i \times R^i, for\ a_i \in {0,...,R-1}$$

By changing R, all radix can be simulated.

# Binary, Octal, Hexadecimal

So for binary, octal and hexadecimal number, they are under R = 2, 8 and 16 respectively. Since number 2 can be dividend of both 8 and 16, we can canvert it easily using some tricky method. Let's say we have a binary number : $1011001101.1011001$
If we want it's octal and hexadecimal version, we can re form those bits into group, each group means the exact value same as the radix, i.e., radix 8 have 0-7 as it digit, then we can merge 3 bit of binary numbers into a group. And the outcome will be like:

Simply is that.