Number Theory > Arithmetic > Number Bases v


Quaternary


The base-4 method of counting in which only the digits 0, 1, 2, and 3 are used. The illustration above shows the numbers 0 to 63 represented in quaternary, and the following table gives the quaternary equivalents of the first few decimal numbers.

1 1 11 23 21 111
2 2 12 30 22 112
3 3 13 31 23 113
4 10 14 32 24 120
5 11 15 33 25 121
6 12 16 100 26 122
7 13 17 101 27 123
8 20 18 102 28 130
9 21 19 103 29 131
10 22 20 110 30 132

These digits have the following multiplication table.

0 1 2 3
0 0 0 0 0
1 0 1 2 3
2 0 2 10 12
3 0 3 12 21

 

Base, Binary, Crumb, Decimal, Hexadecimal, Moser-de Bruijn Sequence, Octal, Ternary




References

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 9-10, 1991.