**A full binary tree *is a combinatorial structure built from an initial point (the root), from which two line segments (called branches, or edges) extend to two new points (called nodes); two further segments extend from each of these, and so on. Successive nodes are arranged in levels: the nodes on level n are those reached from the root by traversing n segments. The nodes on the final level, from which no more branches extend, are the leaves* of the tree.
These definitions closely resemble their counterparts in real trees—the wooden kind. The main formal difference is that, in combinatorics, trees generally have their roots at the top and their leaves at the bottom...
Now label each branch with the route taken to reach it from the root, writing 0 for a move to the left and 1 for a move to the right. This label can be interpreted as the binary representation of a number (see box). Furthermore, at the lower node of each edge, write the value of the corresponding number in base 10. For example, 13 is the decimal form of "1101", the label of the edge reached as follows: starting at the root, first go right (1), then right again (1), then left (0), and finally right (1).
