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                  NPP               Number System, Boolean Algebra and Logic Circuits              251


                      Put one bubble at the output of each OR     àË`oH$ OR JoQ> Ho$ AmCQ>nwQ> na EH$ ~~b bJmVo h¢Ÿ&
                  Gate. One bubbled AND gate is obtained. Con-  Bggo EH$ ~~ëS> AND JoQ> ^r àmßV hmoJmŸ& Bgo NOR
                  vert four NOT Gates into shorted NOR and the
                  bubbled AND gate into NOR. The resulting    JoQ> _| n[ad{V©V H$a gH$Vo h¢Ÿ& gmW hr gmao NOT JoQ>m|
                  logic circuit contains  NOR-NOR Gates only:  H$mo em°Q>}S> NOR _| ~XbZo na:
                                 A       B       C       D














                                                                                       F









                  (e)    The given expression is              (e)    ì`§OH$ F  =  Σm (0, 1, 2, 4) + d (3, 5, 7) hoVw
                         F  =  Σm (0, 1, 2, 4) + d (3, 5, 7)         {ZåZ K-_on àmßV hmoJm:
                         The K-map for the above expression can
                         be drawn as:
                                               A  B C  00  01    11    10


                                               0    1      1     x      1


                                                1   1      x     x      0

                  SOP Form Solution                           SOP \$m°_© gm°ë`yeZ
                      Take the same k-map and make group of         SOP Ho$ ê$n _| hb H$aZo hoVw k-‘¡n br{OE VWm
                  ‘1’.                                        '1' Ho$ g_yh ~ZmVo h¢…

                                                 A  B C  00  01   11     10


                                                  0    1     1     x     1

                                                  1    1     x     x     0
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