Designing Custom Number Systems and Bases

Ever wondered how computers count in binary, or how hexadecimal works under the hood? Moving beyond base-10 opens up a deeper understanding of computer science, data representation, and discrete mathematics. In this text-only course, you will master the foundational mechanics of positional number systems. You will learn how to conceptualize, construct, and convert between custom number systems using your own chosen bases and unique symbol sets. What you'll learn: - Understand the core mathematical principles of positional notation and base systems. - Design custom number systems with unique bases and personalized character sets. - Convert numbers step-by-step between standard bases and your custom systems. - Apply arithmetic operations like addition and multiplication in non-standard bases. - Explore modern real-world applications of custom bases, such as Base64 encoding and cryptography. Starting with fundamental definitions and historical context, this course guides you through the math of bases before walking you through practical, written design challenges. You will practice translating values and defining rules for your own custom systems through clear, step-by-step written exercises. This course is designed for beginners, curious puzzle-solvers, and entry-level computer science students with no advanced math background required. Start reading today to build a stronger foundation in how computers represent and process data.