The binary sequences of length 1 can be listed so that consecutive sequences in the list, including the first and last, differ in exactly one place. One such list is L_1 = 0,1. The binary sequences of length 2 can also be listed so that consecutive sequences in the list, including the first and last, differ in exactly one place. One such list is L_2 = 00,01,11,10. The list. L_2 is constructed from L_1 in several steps. First, let 0 middot L_1 be the list constructed from L_1 by adding a 0 to the left end of every sequence in L_1, so that 0 middot L_1 = 00,01. The list 1 middot L_1 is constructed similarly. Then L_2 consists of the sequence 0 middot L_1 followed by the sequence 1 middot L_1 in reverse order (say L_2 = 0 middot L_1, reverse(1 middot L_1)). (a) Show, by producing the list, that the binary sequences of length 3 can be listed so that consecutive sequences in the list, including the first and last, differ in exactly one place. (b) Prove that, for any n greaterthanorequalto 1, the binary sequences of length n can be listed so that consecutive sequences in the list, including the first and last, differ in exactly one place