# Where does this given info come from? [closed]

I am following this slide on FFT. On the last page, it says:

I would like to ask where $$a = A(2)$$ comes from. Thanks.

• That's the definition of the binary expansion. Jun 9 at 14:34
• What are your thoughts? Jun 9 at 14:38

In base two, a number $$b = b_{n-1}\dots b_0$$ stands for $$b = \sum_{i=0}^{n-1} b_i 2^i$$.
Defining the polynomial $$B(X) =\sum_{i=0}^{n-1} b_i X^i$$, you have $$b = B(2)$$.
Note : in base $$\beta$$, the number $$b = b_{n-1}\dots b_0$$ is $$B(\beta)$$.
• Thanks!!! This clarifies everything. I was wondering what happens if I swap $2$ with something else.