Number Systems
A number system is a method of representing quantities using a consistent set of symbols and rules. The fundamental characteristic of any number system is its base, which determines how many unique digits are available and at what point positional values increment. In a base-n system, each position represents a power of n, and digits range from 0 to n−1. The decimal system (base 10), familiar from everyday use, employs digits 0–9. However, other bases are equally valid and useful for different applications.
Common Number Systems
The binary system (base 2) uses only digits 0 and 1, making it essential for digital computing and information storage. The hexadecimal system (base 16) employs digits 0–9 and letters A–F, and is widely used in programming and computer science because it compactly represents binary values. The octal system (base 8) is occasionally used in computing contexts. Ancient civilizations used various bases: the Babylonians employed base 60 (still reflected in how we measure time and angles), while the Mayans used base 20.
Conversion and Application
Converting between number systems involves expressing a quantity in terms of the powers of the target base. For example, the decimal number 25 equals 11001 in binary (1×16 + 1×8 + 0×4 + 0×2 + 1×1) and 19 in hexadecimal (1×16 + 9×1). Different bases serve different practical purposes: binary underpins all digital systems, hexadecimal aids human readability of machine code, and decimal remains the standard for human arithmetic and commerce.
Source Notes
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- 2026-04-30: Microsoft