The principals of the positional systems.

In order to limit the number of necessary symbols in expressing quantity, people invented positional representation of numbers. The system can use any choosen number as its base. Counted elements are grouped. Every completed group contains the number of objects equal to the base. Objects can be an element or can a smaller identical completed group.Grup can contain only identical objects.

To represent a given quantity the numbers of different kind of completed groups have to be written down from the left to the right starting with the number of the biggest group . If some possible groups are not present, zero is written. Finally the expression is ended by the number of remaining units.

The number of units, any different completed groups contains, is given by the following formula:
g=b^p where g is the number of units, b is the number equal to the given base and p is the current position in the expression counted from the left to the right and started with 0 for the position of units. The number of units in the completed groups at a given position is called the weight of the position.

Example of base three system number: 210=   2 groups of three groups of three, 1 group of three, no units.

2	1	0
ooo     ooo ooo     ooo ooo     ooo	ooo

To understand the notations of any positional number system we have to remember, or be able to resolve using the blue formula, the weight of every position in the notation. That also can be counted knowing that each next to the left position has a weight base time bigger than the previous one.