Information Entropy Problem

Question

I cannot figure out this simple entropy problem and it is driving me crazy!

From McElreath's Statistical Rethinking:

Imagine instead 5 buckets and a pile of 10 individually numbered pebbles. You stand and toss all 10 pebbles such that each pebble is equally likely to land in any of the 5 buckets.

Distribution & Entropy:

A <- (0,0,10,0,0) = 0

B <- (0,1,8,1,0) = 0.6390319

C <- (0,2,6,2,0) = 0.9502705

D <- (1,2,4,2,1) = 1.4708085

E <- (2,2,2,2,2) = 1.6094379

For "B" I did -1[(.1)log2(.1) + (.8)log2(.8) + (.1)log2(.1)] = 0.92

For "E" I did -1[(.2)log2(.2) + (.2)log2(.2) + (.2)log2(.2) + (.2)log2(.2) + (.2)log2(.2)] = 2.32

Where did I go wrong?!?!

Answer 1

It's because the entropy in this exercise is calculated using natural logarithm. For example, for (B), we will have:

$$\mathcal H_B=-2\times 0.1\times \ln(0.1)-0.8\times \ln(0.8)\approx 0.6390$$