This course provides a complete study of number base systems, a core concept in mathematics and computer science. It moves beyond the familiar base 10 system to explore how numbers are represented and manipulated in other bases, such as binary, which forms the foundation of all digital technology. We will cover the principles of different bases, methods for conversion between them, and arithmetic operations within these systems. A command of number bases is non-negotiable for anyone serious about computer science or digital electronics. It is the language of computers. This knowledge is essential for understanding data representation, low-level programming, and network protocols. It provides a deeper appreciation for the structure of the number system we use every day. By the end of this course, you will be able to convert any number from one base to another, including decimal fractions. You will perform addition, subtraction, multiplication, and division in any base with confidence. You will also explain the direct application of the binary system in computer programming. This course is built for secondary school students taking their first formal steps into advanced mathematical concepts. It is also essential for aspiring programmers, computer science students, and electronics enthusiasts who need to understand the fundamental principles of digital systems. No prior knowledge beyond basic arithmetic is required.