The decimal number system

Best known positional number representation:

  • The decimal number system    

Example: (high school stuff)

    423          
	   3 is in ones position (= 3 x 100)
	   2 is in tens position (= 2 x 101)     
	   4 is in tens position (= 4 x 102)
    423
    ^^^
    |||
    ||+--- value =  3  x    1 =    3
    |+---- value =  2  x   10 =   20 
    +----- value =  4  x  100 =  400 +
                             ---------
	 represented value   =   423
   

The decimal number system

What does it really mean:

  423          

  3 represents this value:  •••
  2 represents this value:  ••
  4 represents this value:  ••••

	   3 is in ones position     (= •••  x 100)
	   2 is in tens position     (= ••   x 101) 
	   4 is in hundreds position (= •••• x 102)     

  423
  ^^^
  |||
  ||+--- value =  •••  
  |+---- value =  ••  ••  ••  ••  ••  ••  ••  ••  ••  •• (x 10)
  +----  value =  ••••  ••••    (........)      ••••    (x 100)      
                ---------------------------------------   
	Add up all the dots:  423 dots !!
   

The decimal number system as a representation system for numerical values illustrated
 

The decimal number system is a representation system for (unsigned) numerical values:

The binary number system

The computer (due to electrical switch as memory cell) uses:

  • The binary number system    

Example:

    1011     = value expressed in decimal system ?    

    1011
    ^^^^
    ||||
    |||+--- value =   1  x  20  =   1
    ||+---- value =   1  x  21  =   2
    |+----- value =   0  x  22  =   0
    +------ value =   1  x  23  =   8 +
                                -------
    value expressed in decimal  =  11(10)
   

The binary number system

What does it really mean:

  1011       

  1 represents this value:   
  0 represents this value:          (empty)

  1011
  ^^^^
  ||||
  |||+--- value =   •                       (x 20)
  ||+---- value =   •  •                    (x 21)
  |+----- value =                           (x 22)
  +------ value =   •  •  •  •  •  •  •  •  (x 23)
                ---------------------------------------   
	Add up all the dots:  eleven dots !!
        Eleven expressed in decimal number = 11(10)
   

The binary number system as a representation system for numerical values illustrated
 

The binary number system is also a representation system for (unsigned) numerical values: