Many futuristic technologies, such as Internet of Things or nano-communication, assume that a large number of simple devices of very limited energy and computational power will be able to communicate efficiently via wireless medium. Motivated by this, we study broadcasting in the model of ad-hoc wireless networks of weak devices with uniform transmission powers. We compare two settings: with and without local knowledge about immediate neighborhood. In the latter setting, we prove Ω(nlogn)-round lower bound and develop an algorithm matching this formula. This result could be made more accurate with respect to network density, or more precisely, the maximum node degree Δ in the communication graph. If Δ is known to the nodes, it is possible to broadcast in O(DΔlog2 n) rounds, which is almost optimal in the class of networks parametrized by D and Δ due to the lower bound Ω(DΔ). In the setting with local knowledge, we design a scalable and almost optimal algorithm accomplishing broadcast in O(Dlog2 n) communication rounds, where n is the number of nodes and D is the eccentricity of a network. This can be improved to O(Dlogg) if network granularity g is known to the nodes. Our results imply that the cost of "local communication" is a dominating component in the complexity of wireless broadcasting by weak devices, unlike in traditional models with non-weak devices in which well-scalable solutions can be obtained even without local knowledge.