Definition

1. Noun:
   • A number system is a defined set of symbols and rules for using those symbols to represent numbers. It is a systematic way to write, name, and manipulate quantities.

Usage

• The term number system is used to describe the foundational method of counting and calculation in mathematics and computing.
• It is often modified by an adjective to specify the base, such as "decimal number system," "binary number system," or "hexadecimal number system."
• It functions as a countable noun (e.g., "different number systems," "a number system").

Examples

• The decimal number system, which uses ten digits (0-9), is the most common system in everyday use.
• Computers internally use the binary number system, which has only two digits: 0 and 1.
• Understanding different number systems is fundamental to computer science.
• The ancient Babylonians used a number system based on 60.

Advanced Usage

• "Positional number system": A system where the value of a digit depends on its position. The decimal and binary systems are positional.
• "Base of a number system": Refers to the number of unique digits, including zero, used in the system. For example, base-10, base-2.

Variants and Related Words

• Numeral system: A synonym for number system.
• Notation: A broader term for a system of symbols; a number system is a type of notation for representing numbers.
• Base: (in this context) The fundamental number that defines a number system (e.g., base ten).

Synonyms

• Numeral system
• System of numeration

Related Concepts (Not Phrasal Verbs or Idioms)

• Digit: A single symbol used in a number system.
• Place value: The value of a digit based on its position within a number, a key concept in positional number systems.
• Radix: Another term for the base of a number system.

Noun

1. any notation for the representation of numbers