What are (unsigned) number values
 

Important fact:

  • Numeric values are a universal and intrinsic concept

Universal representation of numeric values:

This representation in cultural independent !!!

Some alternative cultural-dependent representations for unsigned numbers
 

Some alternative cultural-dependent representations for unsigned numbers
 

Some alternative cultural-dependent representations for unsigned numbers
 

Unsigned numeric value and its representation
 

Important fact:

  • Numerical values are intrinsic

    • (Four is four in any culture)

  • A numerical value does not depend on any representation system used

    • (Four can be represented differently in different culture)

We will examine different representations for numbers next.

2 types of representations systems for (unsigned) numbers
 

2 types of representation systems for (unsigned) integers:

  1. Non-positional representation system     
  2. Positional representation system

Non-positional number representation
 

In non-positional representation:

  • The value of a digit (or "digit symbol") is always the same

Example: Roman Numbers 

   I  =  one
   V  =  five
   X  =  ten
   L  =  fifty
   C  =  hundred

Positional number representation
 

In positional representation:

  • The value of a digit (or "digit symbol") depends on its position

Example: Decimal Numbers 

   in   12     the value of the digit 2 is two
   in   24     the value of the digit 2 is twenty

Disadvantage of non-positional number representation
 

Diadvantage:

  • The non-positional representation does not allow easy (simple) arithmetic operations

Example: Roman does not perform addition like this: 

       MVL
    + CXII
   -------

Addition can be performed easily in a positional representation