Calculating Shannon entropy on octet streams can be confusing, especially with those who lack a background in mathematics. It's also not necessary in many cases. A more intuitive calculation, which is also easier to implement, involves calculating the average difference.

An informal description of the algorithm:

Find the absolute difference of each octet, as a numeric value, against its successor. Pad with 0 values where the calculation is impossible.

Exclude the left-most and right-most values.

Take the average of those differences.

An example implementation in Python:

def entropy(data, encoding=None):
if not isinstance(data, bytes):
data = bytes(data, encoding=encoding)
data = list(data)
A = [0] + data
B = data + [0]
diff = [abs(B[i] - A[i]) for i in range(len(data))][1:-1]
return sum(diff) / len(diff)