Page 230 - FUNDAMENTALS OF COMPUTER
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                   230                         Fundamentals of Computers                           NPP


                                    F  =      + A.B.C  + A.B.C  + A.B.C  + A.B.C  + A.B.C  + A.B.C  A.B.C
                      The expression contains seven minterms      Bg ì`§OH$ hoVw {ZåZ K-_on VWm J«wßg ~Zm`m Om
                  and the K-map and the groups can be drawn   gH$Vm h¡:
                  as follows-
                                                 A  B C  00  01    11    10


                                                 0    1      1     1      1


                                                 1    1      1     1      0

                      The simplified expression for three quads   AV… gab ì`§OH$ {ZåZmZwgma hmoJm:
                  can be written as

                                                          F =  A +  B +  C
                   3.25 To Obtain the Solution in POS Form     3.25 POS ñdê$n _| gab H$aZm
                      The solutions which we have obtained in     A^r VH$ {OVZo ^r hb àmßV {H$E JE h¢ g^r SOP
                  previous problems, are in SOP Form. We can  (Sum of product) Ho$ ê$n _| àmßV hþE h¢Ÿ& h_Zo Bg hoVw
                  also  write  the simplified expression in  POS  "1" Ho$ g_yh ~ZmE WoŸ& K-_on go h_ grYo-grYo POS
                  (Product of Sum) form. For getting this, pairs,  (Product of sum) Ho$ ê$n _| ^r hb àmßV H$a gH$Vo
                  quads and octets are formed using 0’s . The fol-  h¢Ÿ& Bg hoVw 0 Ho$ Cn`moJ go gmao g_yh ~ZmZo hm|JoŸ& {ZåZ
                  lowing steps are taken:                     {d{Y AnZmB© Om gH$Vr h¡:
                  (1) Cover all the 0’s in pair, quads and octets.  (1) gmao 0 H$mo noAa, ŠdmS> VWm Am°ŠQ>oQ> Am{X _| H$da
                                                                  H$amo&

                  (2) Go from top to bottom and left to right for  (2) àË`oH$ J«wn _| D$na go ZrMo VWm ~mE§ go XmE§ MbmoŸ&
                      each group.
                  (3) Eliminate the variable which changes its  (3) Omo am{e AnZm _mZ ~XbVr h¡, Cgo hQ>m Xmo &
                      value.
                  (4) If a variable is constant at ‘1’ put a bar and  (4) `{X H$moB© Ma ‘1’ na pñWa h¡ Vmo CgHo$ D$na ~ma
                      if this is constant at ‘0’ do not put a bar. Put  bJmAmo (O¡go  ) AÝ`Wm ZhtŸ& gmao Mam| Ho$ _Ü`
                      ‘+’ between all the constant variables. You            A
                      will get a term for one group.              (+) H$m {M• bJmAmoŸ& Bg Vah `moJ (sum) Ho$ ê$n
                                                                  _| EH$ nX àmßV hmoJmŸ&
                  (5) Put a  ‘ . ’  (dot) between all the terms ob-  (5) gmao nXm| Ho$ _Ü` (.) S>m°Q> bJmH$a POS Ho$  ê$n _|
                      tained.                                     ì`§OH$ àmßV {H$`m OmVm h¡Ÿ&

                       Problem 3.69                                àíZ 3.69
                      Simplify the following Boolean expres-      K- _on {d{Y H$m Cn`moJ H$a {ZåZ hoVw POS Ho$
                  sion in POS Form using K-map method:        ê$n _| gab ì`§OH$ kmV H$amo:
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