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Ad hoc wireless networks and sensor networks have nodes with limited battery power, and broadcasting is an important operation in such networks. In this paper, we consider energy efficient one-to-all and all-to-all broadcast communications in such power constrained networks. It is assumed that nodes have power control and can adjust the range of their transmissions. Given a network of N nodes in a playing field of size D/spl times/D, we establish a lower bound and present a simple scheme for a source-to-all broadcast operation. Using simulations we show that the average energy cost of broadcasting from any source is within 25% of this lower bound in a network of 100 nodes in a 500 m/spl times/500 m and a 1000 m/spl times/1000 m area. In the situation awareness application, each node periodically transmits a small packet of 60 bytes to all other nodes in the network. For this all-to-all broadcast communication, we present a cluster scheme when nodes are allowed to transmit long distances, and a chain based scheme when nodes are limited to short distances. Our schemes for situation awareness significantly improve the life of the network compared to schemes with direct transmissions.