The power consumption of mixed-signal systems featured by an analog front-end, a digital back-end, and with signal processing tasks that can be computed with multiplications and accumulations, is analyzed. An implementation is proposed, composed of switched-capacitor mixed analog/digital multiply-accumulate units in the analog front-end, followed by an A/D converter. This implementation is shown to be superior in respect of power consumption compared to an equivalent implementation with a high-speed A/D converter in the front-end, to execute signal processing tasks that include decimation. The power savings are only due to relaxed requirement on A/D conversion rate, as a direct consequence of the decimation. In a case study of a narrowband FIR filter, realized with four multiply-accumulate units, and with a decimation factor of 100; power saving is 54 times. Implementation details are given, the power consumption, and the thermal noise are analyzed.