Although neural networks are a powerful tool, their widespread use is hindered by the opacity of their decisions and their black-box nature, which result in a lack of trustworthiness. To alleviate this problem, methods in the field of explainable Artificial Intelligence try to unveil how such automated decisions are made. But explainable AI methods are often plagued by missing faithfulness/correctness, meaning that they sometimes provide explanations that do not align with the neural network's decision and logic. Recently, transformations to decision trees have been proposed to overcome such problems. Unfortunately, they typically lack exactness, scalability, or interpretability as the size of the neural network grows. Thus, we generalize these previous results, especially by considering convolutional neural networks, recurrent neural networks, non-ReLU activation functions, and bias terms. Our findings are accompanied by rigorous proofs and we present a novel algorithm RENTT (Runtime Efficient Network to Tree Transformation) designed to compute an exact equivalent decision tree representation of neural networks in a manner that is both runtime and memory efficient. The resulting decision trees are multivariate and thus, possibly too complex to understand. To alleviate this problem, we also provide a method to calculate the ground truth feature importance for neural networks via the equivalent decision trees - for entire models (global), specific input regions (regional), or single decisions (local). All theoretical results are supported by detailed numerical experiments that emphasize two key aspects: the computational efficiency and scalability of our algorithm, and that only RENTT succeeds in uncovering ground truth explanations compared to conventional approximation methods like LIME and SHAP. All code is available at https://github.com/HelenaM23/RENTT .