Machine learning has aided the improvement of medical diagnostic systems that help to detect diseases accurately in the present era. The work gave a mathematical and algorithmic handbook for characteristic selection with a binary Genetic Algorithm (GA) of particular use to jobs involving medical diagnosis. Clinical datasets usually have many dimensions and redundancy, which most time affects model performance and increases computational complexity. In this study is presented a mathematical and algorithmic guide for selecting features through a binary Genetic Algorithm (GA), especially suitable for medical diagnostic tasks. The proposed method seeks to obtain the most informative subset of features by optimizing a fitness function that balances between classification accuracy and dimensionality reduction. The work develops a thorough mathematical model that incorporates data preprocessing, binary encoding of feature subsets, and repetitive evolutionary optimization. The metric used in testing the classification model is standard performance metrics-accuracy, sensitivity, specificity, and F1 score, summarized using a confusion matrix. Understanding feature selection stability across generations is also examined and visualized in a multidimensional performance space. The results would indicate a direct convergence of the model into high-performing feature configurations while avoiding risk for overfitting. An interpretative paradigm, speed-up in computations, as well as high reliability in diagnosis, therefore pushing this method as a tool of great value in clinical decision support systems.