Walks on the binary tree

You have a perfect binary tree of height N. That is, it contains 2N+1 - 1 nodes. A path from the root to a leaf can be represented by an integer X which lies between 0 and 2N - 1 (both inclusive) as follows: Consider the N length binary representation of X. Start reading from the left, and at each bit, 0 denotes going to the left child, and 1 denotes going to the right child. For eg. if N = 2,