An accumulator battery system includes series-connected accumulators with potentials across stages powering corresponding controllers that measure potential differences between terminals of accumulators. A first analog-to-digital converter encodes the potential measured between terminals of an accumulator. A first output delivers a first digital sequence corresponding to the encoded potential difference, logic levels of which are defined by at least two potentials across the first-stage accumulator terminals. A decoder decodes a potential measured by the first control-device from the first digital sequence. A second analog-to-digital converter selectively encodes a potential difference measured between terminals of a second-stage accumulator of the second stage and two potentials of the digital sequence received on the input. A second control-device processor extrapolates a potential difference across the first-stage accumulator terminal of the first stage based on two potentials of the received digital sequence.