Number System
A number system is a writing system for expressing numbers; it is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The basic idea of a number system is to use a small number of symbols that are memorized to represent any number. The numerals are commonly arranged in a numeral system, which is an organized way to represent any number.
Types of Number Systems
Decimal System
The decimal system is the most widely used numeral system, sometimes referred to as the base-10 system. It uses ten symbols: 0 through 9. Each position in a decimal number represents a power of ten. This is the system humans most commonly use for arithmetic computations.
Binary System
The binary number system is used extensively in computer science and digital electronics. It is a base-2 numeral system that utilizes only two symbols: 0 and 1. Every binary number represents a power of two, making it fundamental for the operation of computers.
Factorial Number System
The factorial number system, or factoradic, is a mixed radix numeral system useful in combinatorics, particularly in numbering permutations. It is distinct in that each digit's value is a factorial, unlike conventional positional systems.
Roman Numerals
Roman numerals are a number system originating in ancient Rome, utilizing combinations of letters from the Latin alphabet: I, V, X, L, C, D, and M. Unlike other systems, Roman numerals do not have a symbol for zero and are not typically used for arithmetic.
Indian Numbering System
The Indian numbering system is utilized in countries such as India, Pakistan, and Bangladesh for expressing large numbers. This system incorporates terms like lakh (100,000) and crore (10,000,000), differing from the international system.
Special Purpose Number Systems
Nashville Number System
The Nashville Number System is used in music notation to denote chords based on the scale degree. Developed in Nashville, this system serves as a shorthand for musicians, especially in the country and jazz genres.
Universal Numbering System
The Universal Numbering System is a dental notation used in the United States for identifying teeth. It is sometimes called the "American System" and is part of the standard in dental care documentation.
Vancouver System
The Vancouver system is a citation style that employs a number within the text to denote references. Known as the author-number system, it is widely used in medical and scientific publications.
Historical Development
Historically, numeral systems have evolved alongside the needs of society. Ancient systems such as the Greek and Egyptian numerals lacked a representation for zero, a concept that was later developed in the Indian subcontinent and transmitted to Europe via Arab mathematicians.
The introduction of zero allowed for the development of more complex number systems. The symbol for zero, a round symbol, was first found in Chinese mathematical texts and later adopted in the Mathematical Treatise in Nine Sections of 1247 AD. This innovation paved the way for the representation of negative and large numbers.