Base number systems are methods for representing numbers using a specific set of digits. The most common system is the decimal system, or base-10, which uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Other systems include binary (base-2), which uses 0, 1, and hexadecimal (base-16), which includes 0-9 and A, B, C, D, E, F to represent values. Each base system has its own rules for counting and calculating. For example, in binary, the number after 1 is 10, while in decimal, it is 2. Understanding base number systems is essential in fields like computer science, where binary is fundamental for digital systems and programming.