Learn about number systems, the method for representing numbers. Understand bases like binary, decimal, and hexadecimal with clear examples.
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A number system, also known as a numeral system, is a systematic method for representing numbers using a set of symbols or digits. It provides a consistent framework to express quantities and perform arithmetic operations. Each system is defined by its base, which determines the number of unique symbols used.
The two main components of a number system are its base (or radix) and its set of symbols (digits). The base is the total count of unique digits available in the system. In a positional number system, the value of a digit depends on its position within the number, with each position representing a power of the base.
The most familiar number system is the decimal system (base-10), which uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). For example, the number 123 in base-10 means (1 × 10²) + (2 × 10¹) + (3 × 10⁰). In contrast, computers use the binary system (base-2), which has only two digits (0 and 1).
Different number systems are crucial in various fields. While humans primarily use the decimal system for everyday calculations, the binary system is fundamental to all digital computers and electronics for storing and processing data. Hexadecimal (base-16) and octal (base-8) systems are often used in computer science as a more human-readable representation of binary-coded values.