Several localized broadcasting protocols for ad hoc and sensor networks were proposed recently, with the goal of minimizing the energy consumption, while still guaranteeing a total coverage of the network. Also, several activity scheduling protocols were proposed, which select nodes in a connected dominating set to be active, with the rest of nodes left in sleep mode for energy savings. This article is the first to consider both problems as a single combined one, in which a localized protocol is proposed as a solution. First, each node considers only neighbors whose distance is no greater than the target radius (which depends on the power consumption model used), and neighbors in a localized connected topological structure such as RNG or LMST. Then, a connected dominating set is constructed using this subgraph. Next, nodes not selected for the set are sent to sleep mode (they periodically wake up for sending and receiving messages from associated closest dominating set nodes). Nodes in selected dominating set remain active and apply neighbor elimination based broadcasting (reduced to a subset of dominant neighbors with the help of the RNG or LMST), with transmission range adjusted to their furthest neighbor (in the considered subgraph) not covered by other transmissions. The algorithm has been implemented and compared with a centralized (BIP) and target radius based minimum energy broadcasting (TR-LBOP) protocol (which do not place any node to sleep mode). It is shown that our algorithm requires similar amount of energy for broadcasting as TR-LBOP, but in addition also has energy savings coming from sleep mode status of significant number of nodes. Moreover, our protocol offers the advantage of a smaller latency, since fewer nodes participate in the broadcast.