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NPP               Number System, Boolean Algebra and Logic Circuits              197


                                0             1           0                        C . B . A
                                0             1           1                        C . B . A

                                1             0           0                        C . B . A
                                1             0           1                        C . B . A

                                1             1           0                        C . B . A
                                1             1           1                    A.B.C
                  Fundamental Sum                             \§$S>m_|Q>b `moJ
                      “Fundamental sum for given values of vari-  `h EH$ Eogm `moJ hmoVm h¡ {OgH$m _mZ {H$gr {X`o JE
                  ables is a sum formed such that it is equal to ‘0’  _mZm| hoVw '0' hmoVm h¡ VWm ~mH$s AÝ` _mZm| hoVw '1' .
                  for that set of values only and for all other sets
                  it is equal to ‘1’.”
                      Consider two variables A and B. These vari-  O¡go Xmo am{e`m| A VWm B Ho$ Mma gå^d _mZ ZrMo
                  ables have four sets of values as show in the  Vm{cH$m _| h¡ …
                  table:              NPP
                                                      A          B
                                                      0          0
                                                      0          1
                                                      1          0
                                                      1          1
                      Consider the  third combination  (A  = 1,   O¡go V¥Vr` n§{º$ _| (A = 1 VWm B = 0) h¡, Vmo BgHo$
                  B = 0), the fundamental sum is:             {b`o \§$S>m_|Q>b `moJ Bg àH$ma hmoJm…

                                                         (A +  B )
                      The following steps are taken to form a fun-  {ZåZmZwgma {H$gr \§$S>m_|Q>b `moJ H$mo ~Zm`m OmVm
                  damental sum:                               h¡…
                  1.  Put a bar over a variable which is equal to  1. {Og am{e H$m _mZ '1' h¡, CgHo$ D$na ~ma (-)
                      ‘1’.                                        bJmAmo& AÝ`Wm ZhtŸ&
                  2.  Do not put a bar over a variable which is  2. AJa am{e H$m ‘mZ 0 h¡ Vmo ~ma Z bJmE&
                      equal to ‘0’.
                  3.  Put a + (Plus) sign between all the variables  3. Cnamoº$mZwgma àmßV g^r am{e`m| Ho$ _Ü` `moJ (+)
                      formed with the help of step 1 and 2.       H$m {M• bJmAmoŸ&
                      Applying the above procedure four funda-    Cnamoº$ {d{Y H$m  Cn`moJ  H$a h_ {ZåZmZwgma
                  mental sums are obtained as shown below in  \§$S>m_|Q>b `moJ àmßV H$a gH$Vo h¢…
                  the table:
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