Overview: the different kinds of data stored in a computer
 

 

We will study how unsigned integer numbers are represented inside a computer next

What are (unsigned) integer values
 

Important fact:

  • Integer (= whole number ) values are a universal and intrinsic concept

Universal way to represent unsigned integer values:

This way to represent numeric values is cultural independent !!!

Some cultural-dependent representations for unsigned numbers
 

The Ancient Romans use (some) of the letters of the alphabet to represent numeric values: 

   I, II, III, IV, V, 

   VI, VII, VIII, IX, X, 

   XI, XII, XIII, XIV, XV, ....     

   I = one
   V = five
   X = ten
   L = fifty
   C = one hundred
   D = five hundred
   M = one thousand

The concept and the Roman representation for numerical value illustrated

Some cultural-dependent representations for unsigned numbers
 

The Chinese use the following characters (symbols) represent numeric values:

 

The concept and the Chinese representation for numerical value illustrated

Some cultural-dependent representations for unsigned numbers
 

The Egyptians use the following characters (symbols) represent numeric values:

 

= 1 = 10 = 100 = 1000
= 10000 = 100000 = 1000000

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 in the number

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: Romans do not perform additions like this: 

       MVL
    + CXII
   -------

Addition can be performed easily in a positional representation