Network coding over a delay-free acyclic communication network with single source is considered in this paper. The network is modeled as a directed acyclic graph G where each edge in G is assumed to have unit link capacity. Previous works on network coding require a sufficiently large field such that the network has either a linear multicast, a linear broadcast, or a linear dispersion solution. For certain graphs, it is also known that linear network codes over a field of smaller size might not exist. In this paper, we propose a linear network code with memory and show that for any directed acyclic network with single source, there always exists a binary linear dispersion network code. Such code can be explicitly constructed and requires only the binary field for realization. Thus, this approach would dramatically reduce the hardware complexity for code implementation. Also contained in this paper is an explicit construction of binary linear broadcast network code for any directed acyclic networks.