Countable v. Uncountable:

Prove that B*, the set of all finite strings over B = {0; 1} is countable, that is, B* can be put in a one-to-one correspondence with the natural numbers N = {0, 1, 2,3,.....}. Hint: List the strings in B* in order of increasing length. Notice where the strings reset to all 0s.

strings |lambda 0 1 00 01 10 11 000 001 010 011 100 101 110 111 0000 0001

binary |0 0 1 0 1 2 3 0 1 2 3 4 5 6 7 0 1

n N |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Please explain me the solution