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This paper considers the problem of estimating the power consumption at logic and register-transfer levels of design from an information theoretical point of view. In particular, it is demonstrated that the average switching activity in the circuit can be calculated using either entropy or informational energy averages. For control circuits and random logic, the output entropy (informational energy) per bit is calculated as a function of the input entropy (informational energy) per bit and an implementation dependent information scaling factor. For data-path circuits, the output entropy (informational energy) is calculated from the input entropy (informational energy) using a compositional technique which has linear complexity in terms of the circuit size. Finally, from these input and output values, the entropy (informational energy) per circuit line is calculated and used as an estimate for the average switching activity. The proposed switching activity estimation technique does not require simulation and is thus extremely fast, yet produces sufficiently accurate estimates