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We numerically demonstrate two types of metasurface absorbers to efficiently absorb digital signals. First, we show that the digital waveforms used in this study contain not only a fundamental wave but also nonnegligible harmonic waves, which limits the absorption performance of a conventional metasurface absorber operating in only a single, finite frequency band. The first type of the proposed absorbers is designed using two kinds of unit cells, each of which absorbs either a fundamental frequency or third harmonic of an incident digital waveform. This dual-band metasurface absorber exhibits absorption performance exceeding that of the conventional metasurface absorber and more strongly dissipates the energy of a digital waveform. In addition, the second type of absorber exploits the concept of nonlinear analogous circuits to convert an incoming wave to a different waveform, specifically, a triangular waveform that has a larger magnitude at a fundamental frequency. Therefore, the incoming waveform is more effectively absorbed by this waveform-conversion metasurface absorber as well. Although still there remain some issues to put these digital signal absorbers into practice, including experimental validation, our results contribute to mitigating electromagnetic interference issues caused by digital noise and realising physically smaller, lighter digital signal processing products for the next generation.