Hamming Distance Matrix

Design a hardware module for the Hamming Distance Matrix problem.

Given a stream of unsigned 32-bit vectors, use the first 8 vectors and output the pairwise Hamming distance matrix for an 8 by 8 grid.

If fewer than 8 vectors are provided, treat the missing entries as zero. If more than 8 vectors are provided, ignore the extras.

Hardware I/O Encoding

• vectors is a one-dimensional stream of unsigned 32-bit integers
• the output is a two-dimensional stream of unsigned 6-bit integers
• output row i, column j is the number of differing bit positions between vector i and vector j
• rows and columns both run from 0 to 7

Example

• input vectors = [10, 12, 3]
• the top-left 3 x 3 block of the output is [0, 2, 2], [2, 0, 4], [2, 4, 0]

The remaining rows and columns use 0 for the missing vectors.