In dynamic environments where new concepts continuously emerge, Deep Neural Networks (DNNs) must adapt by learning new classes while retaining previously acquired ones. This challenge is addressed by Class-Incremental Learning (CIL). This paper introduces Generative Binary Memory (GBM), a novel CIL pseudo-replay approach which generates synthetic binary pseudo-exemplars. Relying on Bernoulli Mixture Models (BMMs), GBM effectively models the multi-modal characteristics of class distributions, in a latent, binary space. With a specifically-designed feature binarizer, our approach applies to any conventional DNN. GBM also natively supports Binary Neural Networks (BNNs) for highly-constrained model sizes in embedded systems. The experimental results demonstrate that GBM achieves higher than state-of-the-art average accuracy on CIFAR100 (+2.9%) and TinyImageNet (+1.5%) for a ResNet-18 equipped with our binarizer. GBM also outperforms emerging CIL methods for BNNs, with +3.1% in final accuracy and x4.7 memory reduction, on CORE50.