CS255 Sylabus

Positional value representation systems

Best known positional system is decimal number system

Value of a digit depends on its position in number:

There are 10 digits in use: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Value of digits increase by 10 for each position
Hence it is called the decimal (10) number system

  Example:

               679          
			6 is in hundreds position (600)
			7 is in tens position (70)
			9 is in ones position (9)
               679
               ^^^
	       |||
	       |||
	       ||+--- value at   1: 9 x   1 =    9
	       |+---- value at  10: 7 x  10 =   70
	       +----- value at 100: 6 x 100 =  600 +
                                            --------
			represented value   =  679

The computer uses the binary number system:

Value of a digit depends on its position in number:

There are 2 digits in use: 0, 1
Value of digits increase by 2 for each position
Hence it is called the binary (2) number system

Example 1:


               1011          
               ^^^^
	       ||||
	       |||+-- value at 1: 1 x 1 =    1
	       ||+--- value at 2: 1 x 2 =    2
	       |+---- value at 4: 0 x 4 =    0
	       +----- value at 8: 1 x 8 =    8 +
                                         --------
		    represented value   =   11  (decimal)

Example 2:


              11001          
              ^^^^^
	      |||||
	      ||||+-- value at  1: 1 x  1 =    1
	      |||+--- value at  2: 0 x  2 =    0
	      ||+---- value at  4: 0 x  4 =    0
	      |+----- value at  8: 1 x  8 =    8
	      +------ value at 16: 1 x 16 =   16 +
                                           --------
		      represented value   =   25  (decimal)