Page 11 - Computer Genius Class 07
P. 11

The  alue o  a num er is determined  y multiplying the digits  ith the  eight o  their position and
                 adding the results. This method is  no n as expansion method. The right most digit o  the num er
                 has the lo est  eight. This digit is called Least Significant Digit  LSD . The le t most digit o  a
                 num er has the highest  eight. This digit is called Most Significant Digit  MSD . The digit   in the
                 num er  2  is the most significant digit and   is the least significant digit.
                 The gi en ta le sho s positional  eight o  decimal num er   2   .
                                                                                   1

                                                          Hundereds             Tens             Units


                         Weights                              1  2              1  1              1

                         Real Value of each digit               1  2           2   1  1              1

                         Result                                                  2

                 Binary Number System

                 The  ord   inary  comes  rom   i  meaning t o.  e see   i  in  ords such as   icycle   t o  heels
                 or   inocular   t o eyes . The  inary num ers ha e the  ase o  2.
                 A computer is a machine made up o  transistors  s itches and other components. All these electronic
                 components are in t o mutually e clusi e states  either O  or OFF. The t o  inary digits represent
                 these t o states.   ery instruction gi en to a computer is con erted into   s and 1 s so that it can  e
                 understood and implemented  y the computer.  inary language is there ore  no n as the machine
                 language.
                 A  inary num er is made up o  only 0s and 1s.        Name     Size (bits)         Examples

                   ample o   inary  um er  110100
                                                                      it            1      Single digit either   or 1
                 There is no 2                   or   in  inary
                                                                      i  le                 roup o    digits
                  et us first learn ho  to  orm  inary num ers.
                                                                      yte                   roup o    digits
                 As  the   inary  num er  system  consists  o   t o
                                                                      ord          1        roup o  1  digits
                 digits   and 1 hence  its  ase is 2.  ach digit or
                  it in  inary num er system can  e   or 1. A com ination o   inary digits may  e used to represent
                 different  uantities li e 1  1. The positional  alue o  each digit in  inary num er is t ice the place
                  alue or  ace  alue o  the digit o  its right side. The  eight o  each position is a po er o  2.
                 The place  alue o  the digits according to position and  eight is as  ollo s


                           Position                 2         1                              1          2

                           Weights        2         2 2       2 1       2                   2  1      2  2





                   A single  inary digit  li e     or  1   is called a   it . For e ample 11 1  is fi e  its long. The  ord
                    it is made up  rom the  ords   inary digit .



                                                                                            Number System      9
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