As is well known, any real in [0,1] can be written as a binary expansion in base 1/2:

```
x = b1 * 1/2^1 + b2 * 1/2^2 + ...

```

I would like an efficient way to get **bi** for a given **x** and index **i**, and I don't think there's any built-in way to do that in Mathematica. IntegerDigits and RealDigits don't seem to be able to help, and none of the related functions are pertinent.

The obvious solution is to do the manual conversion, but I was hoping to avoid that. Am I missing something? 

**EDIT**: for future reference, what I was looking for can be done this way,

```
BinaryExpansionBit[p, j] := RealDigits[p, 2, 1, -j][[1]][[1]]

```

where

```
BinaryExpansionBit[x, i]

```

gives the **bi** I was talking about.