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Energy efficiency is a key requirement in the design of wireless sensor networks. While most theoretical studies only account for the energy requirements of communication, the sensing process, which includes measurements and compression, can also consume comparable energy. In this paper, the problem of sensing and communicating parallel sources is studied by accounting for the cost of both communication and sensing. In the first formulation of the problem, the sensor has a separate energy budget for sensing and a rate budget for communication, while, in the second, it has a single energy budget for both tasks. Furthermore, in the second problem, each source has its own associated channel. Assuming that sources with larger variances have lower sensing costs, the optimal allocation of sensing energy and rate that minimizes the overall distortion is derived for the first problem. Moreover, structural results …