In this paper, we investigate the application of early-exit strategies to quantized neural networks with binarized weights, mapped to low-cost FPGA SoC devices. The increasing complexity of network models means that hardware reuse and heterogeneous execution are needed and this opens the opportunity to evaluate the prediction confidence level early on. We apply the early-exit strategy to a network model suitable for ImageNet classification that combines weights with floating-point and binary arithmetic precision. The experiments show an improvement in inferred speed of around 20% using an early-exit network, compared with using a single primary neural network, with a negligible accuracy drop of 1.56%.