Number Systems

 A Number System is a set of numbers. The numbers are the  System Elements of the Number System.

The Number System can be understood with the help of Number System Elements. The Number System Elements are the structural units of the Number System.

The number of distinct symbols that are used to design a Number System decides the nomenclature of the Number System. The cardinality of Number System Elements is called the base, or radix of the Number System. 

The Binary Number System has a base equal to two. This means that there are two distinct symbols in the Binary Number System. The two unique symbols that are used to frame Binary Numbers are: '0', and '1'. 

'0' and '1' are the symbols that are used in the Binary Number System. 

Likewise the Decimal Number System has a base equal to ten. So, there are ten distinct symbols (digits) that are used to structure a decimal number. 

The symbols that are employed in a Number System are called numerals. These numerals help us to numerate.

We can construct a System of numbers using the Number System. The Number System Elements are the fundamental units of such a System.

'0' and '1' are the fundamental structural units of Binary Numbers. These fundamental units are called Binary Number System Elements.

The Decimal Number System Elements are: '0', '1', '2', ….., '9'.

Each Number System Element of a Number System distinctly seeks to quantify. The Element is precisely associated with a quantity.

The Number System Elements provide primitive support. In fact, the standalone Elements support quantification in the most fundamental terms. 

The cardinality of unique symbols that are fundamentally supported is equal to the base of the Number System.

Using Number System Elements  a System of numbers can be constructed. Many times such a     System  just seeks to quantify. In such a case the order of numbers may be ignored.

There are times when a System of numbers is used to specify an order. When numbers are used to express ordinality of an object series, the values that are associated with the numbers are the determinants of series structure. 

A Number System may be a Positional System. The value of a number in a Positional System is determined by the positions of the digits (Number System Elements) that form the number. In other words, the position occupied by a digit in the  number determines the value of Number System Element.

Either ascending, or descending order can describe a series of numbers.