Based on the base value and the number of allowed digits, number systems are of many types. The four common types of Number Systems are: 1

A number system can be considered as a mathematical notation of numbers using a set of digits or symbols. In simpler words the number system is a method of representing numbers. Every number system is identified with the help of its base or radix. For example, Binary, Octal, Decimal and Hexadecimal Number systems are used in microprocessor programming. 2
In mathematics, a “base” or a “radix” is the number of different digits or combination of digits and letters that a system of counting uses to represent numbers.
Wikipedia
One additional number system that should be understood is the Sexagesimal Number System.
References
1 “Number System In Maths – GeeksForGeeks”. 2020. GeeksForGeeks. https://www.geeksforgeeks.org/number-system-in-maths/.
2 “Decimal Number System – Geeksforgeeks”. 2020. Geeksforgeeks. https://www.geeksforgeeks.org/decimal-number-system/.
Additional Reading
“Number System In Computer, Binary, Octal, Decimal, Hexadecimal”. 2020. Electronic Clinic. https://www.electroniclinic.com/number-system-in-computer-binary-octal-decimal-hexadecimal/.
Tawde, Swati. “Number Systems | Top 4 Types Of Number Systems (Examples)”. 2020. EDUCBA. https://www.educba.com/number-systems/.