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#ENTROPY SYMBOL HOW TO#
Interestingly, using log identities, you can work out how to convert the resulting entropy between units. Using b=256 will give the result in bytes, as each byte can have one of 256 discrete values. Using b=10 puts the result in dits, or decimal bits, as there are 10 possible values for each dit. Using b=2 allows a result in bits, as each bit can have 2 values. It is possible to use other logarithm bases.
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When the bytes of a file are evenly distributed, you'll find that there is an entropy of 8 bits. Try it yourself: maximize the entropy of the input by making byte_counts a list of all 1 or 2 or 100. In such a case, you have a maximum of 8 bits of entropy for any given file. It is true that this algorithm is usually applied using log base 2. The resulting value will be between 0 (every single byte in the file is the same) up to 1 (the bytes are evenly divided among every possible value of a byte).Īn explanation for the use of log base 256 A byte composed of eight bits will have 256 possible values. The 256 in the call to math.log represents the number of discrete values that are possible. If count = 0, then p = 0, and log( p) will be undefined ("negative infinity"), causing an error. The check for count = 0 is not just an optimization. There are several things that are important to note. # p is the probability of seeing this byte in the file, as a floating. # If no bytes of this value were seen in the value, it doesn't affect I'll write the following code in Python, but it should be obvious what's going on. Total is the total number of bytes in your file. For example, byte_counts is the number of bytes that have the value 2. The following variables are assumed to already exist:īyte_counts is 256-element list of the number of bytes with each value in your file. (tydok's answer works on a collection of bits.) To calculate the information entropy of a collection of bytes, you'll need to do something similar to tydok's answer.