To calculate the minimum Hamming distance between two arrays, we need to count the number of positions in which the corresponding bits differ. In other words, we need to count the number of "1" bits in the result of the XOR operation between the two arrays.
(a) 001 ^ 010 = 011
The Hamming distance is 2, since there are two positions in which the corresponding bits differ.
(b) 0010 ^ 0100 = 0110
The Hamming distance is 2, since there are two positions in which the corresponding bits differ.
(c) 011 ^ 010 = 001
The Hamming distance is 1, since there is only one position in which the corresponding bits differ.
(d) 0101 ^ 0010 = 0111
The Hamming distance is 3, since there are three positions in which the corresponding bits differ.
(e) 010 ^ 110 = 100
The Hamming distance is 2, since there are two positions in which the corresponding bits differ.
Therefore, the minimum Hamming distances for each pair of arrays are:
(a) 2
(b) 2
(c) 1
(d) 3
(e) 2