A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. Such an understanding would be of great benefit when attempting to build a quantum computer. Here we present a framework that uses classical resources but still is able to efficiently run, for example Deutsch-Jozsa and Simon's algorithms, and also can run Shor's factoring algorithm with some systematic errors. We also perform an experiment factoring 15 using classical pass-transistor logic at room temperature, with smaller systematic errors than any former experimental implementation, and the same amount of resources in time and space as a scalable quantum computer. Our results give further insight into the resources needed for quantum computation, aiming for a true understanding of the subject.