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The goal of conversational machine reading is to answer user questions given a knowledge base text which may require asking clarification questions. Existing approaches are limited in their decision making due to struggles in extracting question-related rules and reasoning about them. In this paper, we present a new framework of conversational machine reading that comprises a novel Explicit Memory Tracker (EMT) to track whether conditions listed in the rule text have already been satisfied to make a decision. Moreover, our framework generates clarification questions by adopting a coarse-to-fine reasoning strategy, utilizing sentence-level entailment scores to weight token-level distributions. On the ShARC benchmark (blind, held-out) testset, EMT achieves new state-of-the-art results of 74.6% micro-averaged decision accuracy and 49.5 BLEU4. We also show that EMT is more interpretable by visualizing the entailment-oriented reasoning process as the conversation flows. Code and models are released at https://github.com/Yifan-Gao/explicit_memory_tracker.