A counting system is a mathematical idea that orders numerals in a way that they can be used to count and to perform various mathematical operations. In mathematics, there are many different counting systems, sometimes called number systems.
The counting system most common for everyday use is known as base 10. Base 10 is a fancy math term for what people have likely been doing since they have had fingers and toes: ordering from 1 to 10, then bundling that group of ten. So, two groups of ten (like toes and fingers) equals twenty, ten groups of ten equals one hundred, and so on.
Another counting system that is common but people do not typically use to count, say, apples and oranges, is the binary system. The binary system, or base 2, is comprised solely of 0’s and 1’s. The binary, base 2 system is used primarily in computing.
Below are a few interesting references and study materials for number systems. Have fun!