Designing a circuit that calculates Hamming distance?
"the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different." (Wiki)

Simple approach: compare the bits pairwise using XOR (output is 1 when the inputs differ) and add the outputs of the XORs using a string of adders.

This will work, but there is probably a simpler way to add a bunch of 1's and 0's than using full adders.

I am not sure I agree with the WiKi definition, to me Hamming distance is a property of an encoding (a subset of valid values, within a larger set of possible values). An encoding (or a subset) is a mathematical construct, not a physical value, so you can't input it to a digital circuit.