Frequent counting is a very so often required operation in machine learning algorithms. A typical machine learning task, learning the structure of Bayesian network (BN) based on metric scoring, is introduced as an example that heavily relies on frequent counting. A fast calculation method for frequent counting enhanced with two cache layers is then presented for learning BN. The main contribution of our approach is to eliminate comparison operations for frequent counting by introducing a multi-radix number system calculation. Both mathematical analysis and empirical comparison between our method and state-of-the-art solution are conducted. The results show that our method is dominantly superior to state-of-the-art solution in solving the problem of learning BN. Frequent counting is a very so often required operation in machine learning algorithms. A typical machine learning task, learning the structure of Bayesian network (BN) based on metric scoring, is introduced as an example that heavily relies on frequent counting. A fast calculation method for frequent counting enhanced with two cache layers is then presented for learning BN. The main contribution of our approach is to exclude comparison operations for frequent counting by introducing a multi-radix number system calculation. Both mathematical analysis and empirical comparison between our method and state -of-the-art solution are conducted. The results show that our method is dominantly superior to state-of-the-art solution in solving the problem of learning BN.