Encoding the shape of a binary tree is a basic step in a number of algorithms in integrated circuit design, automated theorem proving, and game playing. We propose cost-optimal parallel algorithms to solve the binary tree encoding/decoding problem. Specifically, we encode the relevant shape information of an n-node binary tree in a 2n bitstring. Conversely, given an arbitrary 2n bitstring we reconstruct the shape of the corresponding binary tree, if such a tree exists. All our algorithms run in O (log n) time using O (n/log n) processors in the EREW-PRAM model of computation.