Kerr soliton microcombs have the potential to disrupt a variety of applications such as ultra-high-speed optical communications, ultra-fast distance measurements, massively parallel light detection and ranging (LiDAR) or high-resolution optical spectroscopy. Similarly, ultra-broadband photonic-electronic signal processing could also benefit from chip-scale frequency comb sources that offer wideband optical emission along with ultra-low phase noise and timing jitter. However, while photonic analogue-to-digital converters (ADC) based on femtosecond lasers have been shown to overcome the jitter-related limitations of electronic oscillators, the potential of Kerr combs in photonic-electronic signal processing remains to be explored. In this work, we demonstrate a microcomb-based photonic-electronic ADC that combines a high-speed electro-optic modulator with a Kerr comb for spectrally sliced coherent detection of the generated optical waveform. The system offers a record-high acquisition bandwidth of 320 GHz, corresponding to an effective sampling rate of at least 640 GSa/s. In a proof-of-concept experiment, we demonstrate the viability of the concept by acquiring a broadband analogue data signal comprising different channels with centre frequencies between 24 GHz and 264 GHz, offering bit error ratios (BER) below widely used forward-error-correction (FEC) thresholds. To the best of our knowledge, this is the first demonstration of a microcomb-based ADC, leading to the largest acquisition bandwidth demonstrated for any ADC so far.