Title: TT-Rules: Extracting & Optimizing Exact Rules of a CNN-Based Model - Application to Fairness. Abstract: Most Machine Learning (ML) models are ``black box'' models, but in critical domains such as healthcare, energy, finance, military, or justice, they need to be globally and exactly interpretable. Creating ML models convertible by design into rule-based models is an attractive solution: they produce all the rules (global nature of interpretability) that allow us to obtain exactly the output result (exact nature of interpretability). Today, these rule-based models are mainly decision trees, whose natural interpretability is outweighed by their poor performances and scalability. In this paper, we offer a new three-step framework, TT-rules, that extracts and optimizes exact rules from a recent family of Convolution Neural Networks (CNNs) called Truth Table nets (TTnets). First, we show how to extract rules $\mathcal{R}$ in Disjunction Normal Form (DNF) from TTnets, which we adapt and enhance for tabular datasets. Secondly, we explain how the TT-rules framework permits the optimization of two key interpretability factors, namely the number of rules and their size, transforming the original set $\mathcal{R}$ into an optimized $\mathcal{R}_{opt}$. Our rule-based model is thus composed of $\mathcal{R}_{opt}$ with a final binary linear regression and allows multi-label classification. In a third step, we improve the rules' visualization by converting them into Reduced Ordered Binary Decision Diagrams (ROBDD) and enriching them by computing interesting associated probabilities. To evaluate TT-rules' performances, we applied it to two tabular healthcare datasets and two fairness datasets. Our framework reaches competitive results compared to state-of-the-art rule-based models in terms of accuracy, complexity, and statistical parity, also giving exact and global interpretability. In addition, we show that practitioners can use their domain knowledge to diagnose individual fairness of a given TT-rules model by analyzing and further modifying the rules $\mathcal{R}_{opt}$. As an example of the compactness of our framework's output, we draw all the rules in $\mathcal{R}_{opt}$ for one model on the Adult dataset (only 15 conditions for an 84.6\% accuracy).