root)level has at most two nodes (the children of the root)level has at most four nodesand so on (see figure in generallevel has at most nodes figure maximum number of nodes in the levels of binary tree we can see that the maximum number of nodes on the levels of binary tree grows exponentially as we go down the tree from this simple observationwe can derive the following properties relating the height of binary with its number of nodes detailed justification of these properties is left as an exercise ( - proposition let be nonempty binary treeand let nn and denote the number of nodesnumber of external nodesnumber of internal nodesand height of trespectively then has the following properties + < < + - <= <= <= <= - log( + )- <= <= - alsoif is properthen has the following properties