<![CDATA[Binary Search is one of the most fundamental and efficient algorithms in computer science, operating on the principle of Decrease and Conquer. This literature review systematically examines the theoretical foundations, variations, complexity characteristics, and practical applications of Binary Search. By analyzing a wide range of academic studies and textbooks, this paper discusses the algorithmic structure, pseudocode, step-by-step illustrations, and time complexity proofs of Binary Search. Additionally, the review explores variants such as Interpolation Search and Exponential Search that extend the core binary search paradigm. The review further investigates real-world applications in database indexing, information retrieval, and software engineering. Results from the literature confirm that Binary Search achieves O(log n) time complexity, making it significantly more efficient than linear search for large sorted datasets. This review aims to provide a comprehensive reference for researchers and practitioners interested in search algorithm design and analysis]]>
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