Let v and u be vectors of the same size with 8-bit integers (0-255). We want to compute the number of bits where those vectors differs i.e. a Hamming distance between vectors formed by concatenation of binary representations of those numbers. For example:

v = [1 0]
u = [1 255] 

Binary representations:

v_bin = [00000001 00000000]
u_bin = [00000001 11111111]

And the Hamming distance:

d = 0 + 8 = 8

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