A number system, also known as a numeral system, is a way of representing numbers using a specific set of symbols or digits. Different number systems use different symbols and bases to represent numbers. The most commonly used number systems are:

Decimal Number System (Base 10): This is the number system most commonly used by humans. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit’s position in a number represents a power of 10. For example, in the number 247, the 2 represents 2 * 10^2, the 4 represents 4 * 10^1, and the 7 represents 7 * 10^0.

Binary Number System (Base 2): In the binary system, there are only two digits: 0 and 1. Each digit’s position represents a power of 2. It’s commonly used in computing because digital electronic devices naturally work with binary values.

Octal Number System (Base 8): The octal system uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit’s position represents a power of 8. It’s less common today but was used in older computer systems.

Hexadecimal Number System (Base 16): The hexadecimal system uses sixteen digits: 09 and AF (where A=10, B=11, C=12, D=13, E=14, and F=15). Each digit’s position represents a power of 16. Hexadecimal is widely used in computing for its compact representation of binary data.

Roman Numerals: Roman numerals are a different kind of number system that uses combinations of letters from the Latin alphabet, such as I, V, X, L, C, D, and M. Roman numerals were used extensively in ancient Rome and are still used today in specific contexts, such as in the names of monarchs and on clock faces.

Other Number Systems: There are many other number systems with various bases and symbols, but these are the most common ones. For example, the ternary system (base 3) uses digits 0, 1, and 2, and the duodecimal system (base 12) uses digits 09 and two additional symbols.
Each number system has its own rules for representing numbers and performing arithmetic operations. The choice of which number system to use depends on the specific application and the convenience of representing and manipulating numbers in that system.