The History of Mathematics

Early Counting and Numbers

What are the names of the various base systems?

The base 10 system is often referred to as the decimal system. The base 60 system is called the sexagesimal system. (This should not be confused with the sexadecimal system—also called the hexadecimal system—or the digital system based on powers of 16.) A sexagesimal counting table is used to convert numbers using the 60 system into decimals, such as minutes and seconds.

The following table lists the common bases and corresponding number systems:

Base Number System
2 binary 9 nonary
3 ternary 10 decimal
4 quaternary 11 undenary
5 quinary 12 duodecimal
6 senary 16 hexadecimal
7 septenary 20 vigesimal
8 octal 60 sexagesimal


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