I did made a minor mistake by not stating that the FALSE example is n=4. ((1<<4) makes 1000, (1<<3) makes 0100) From what I understand from your post you read the bits from left to right. But bits are to be read from right to left, and the remaining 0's are actually redundant.

0001 = 1 = 1
0010 = 10 = 2
0011 = 11 = 3
0100 = 100 = 4
0101 = 101 = 5
...