We study the problem of parallel implementation of divide-and-conquer algorithms on binary de Bruijn network. We model the divide-and-conquer algorithm as a temporal binomial tree computation structure which we show to be an efficient structure for this type of algorithms. We then discuss the problem of mapping such task structures (assigning tasks to processors and routing messages through communication channels) to a binary de Bruijn network of the same size. Two cases are considered where message volumes are of uniform and logarithmically decreasing (increasing) weights. A single mapping is proposed for both cases and the mapping has average extra dilation 1 and is communication link contention-free. A lower bound for the total extra dilation of any mapping from uniform-weighted binomial tree to an arbitrary degree-4 network (a binary de Bruijn network has degree 4) is also developed to show that the mapping is asymptotically optimal with respective to the average extra dilation. The mapping is well suited to a binary de Bruijn network with a wormhole or circuit switching communication scheme.