The semantic framework for the modal logic of knowledge due to Halpern and Moses provides a way to ascribe knowlegde to agents in distributed and multiagent systems. In this paper we study two special cases of this framework: <italic>full systems<italic> and <italic>hypercubes</italic>. Both model static situtations in which no agents has any information about another agent's state. Full systems and hypercubes are an appropriate model for the initial configurations of many systems of interest. We establish a correspondence between full systems and hypercube systems and certain classes of Kripke frames. We show that these classes of systems correspond to the same logic. Moreover, this logic is also the same as that generated by the larger class of <italic>weakly directed frames</italic>. We provide a sound and complete axiomatization, S5WD<italic><subscrpt>n</subscrpt></italic> of this logic, and study its computational complexity. Finally, we show that under certain natural assumptions, in a model where knowledge evolves over time, S5WD<italic><subscrpt>n</subscrpt></italic> characteristics the properties of knowledge not just at the initial configuration, but also at all later configurations. In this particular, this holds for <italic>homogeneous broadcast systems,</italic> which capture settings in which agents are intially ignorant of each others local states, operate synchronously, have perfect recall, and can communicate only by broadcasting.