What does $\operatorname{bb}()$ mean in information theory?

Question

I'm coming across a lot of formulas in the textbook that use "bb()" however, I don't know what bb is, it isn't mentioned anywhere.

For example max entropy in a binary source:

$$\mathbb{H}_{max} = \sum_{j=1}^m \frac1m \cdot \operatorname{bb} \frac1{\frac1m} = \operatorname{bb} m$$

What does the $\operatorname{bb}$ mean?

Edit here is another formula of entropy:

$$\mathbb{H} = \sum_{j=1}^m P_jS_j = \sum_{j=1}^m P_j \cdot \operatorname{bb} \frac1{P_j}$$

With $S_j =$ auto information.

Answer 1

$$bb(x)=log_2(x)$$ is the "binary base" , the logarithm to base $2$.