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NPP               Number System, Boolean Algebra and Logic Circuits              199


                      There are two 1s in the output. First ‘1’ cor-  AmCQ>nwQ> _| Xmo "1" h¢ AV… Xmo {_ÝQ>_© àmßV hmoJr Ÿ&
                  responds to (01) and therefore the fundamental  àW_ {_ÝQ>_© (01) Ho$ gmnoj hmoJr VWm {ÛVr` (11) Ho$
                  product is  .A B . Similarly, for second ‘1’ the fun-  gmnoj `o  .A B  VWm A.B hmoJr Ÿ&
                  damental product is A.B. Thus, the expression
                  Y has two minterms,  .A B  and A.B.
                      Minterms are represented by m  where n      {_ÝQ>_© H$mo m  Ho$ ê$n _| àX{e©V H$aVo h¢ Ohm± na
                                                  n
                                                                            n
                  is the decimal equivalent of the corresponding  n g§~§{YV ~mBZar g§»`m H$m Xe_bd Vwë` h¡Ÿ& O¡go
                  binary number. In the above example the first  Cnamoº$ Vm{bH$m _| àW_ BZnwQ> ~mBZar g§»`m 01 BgH$m
                  binary value is (01). Its decimal is 1. Thus, the  S>ogr_b 1 h¡Ÿ& AV: {_ZQ>_©  A  H$mo  m Ho$ ê$n go
                  minterm  .A B can be represented as m . There-  àñVwV {H$`m Om gH$Vm h¡Ÿ& AV: B .  1
                                                    1
                  fore:
                                                 m =  A  B .  and   Similarly, m  = A.B
                                                   1
                                                                          3
                       Problem 3.52                                àíZ 3.52
                      For  the  given table identify all  the     Vm{bH$m hoVw gmar {_ÝQ>_© àmßV H$s{OE…
                  minterms:
                                                  B
                                  A   NPP                              C              F
                                   0              0                    0              0
                                   0              0                    1              1
                                   0              1                    0              0
                                   0              1                    1              1
                                   1              0                    0              1
                                   1              0                    1              0
                                   1              1                    0              0
                                   1              1                    1              1
                  Solution:                                   hc:
                      There are four 1s in the output. Therefore  My±{H$  AmCQ>nwQ> _| Mma 1 h¢ AV…  Mma {_ÝQ>_©
                  the minterms are:
                                                              {ZåZmZwgma hmoJr…
                                               m =      C . B . A  , m =  C . B . A  ,
                                                 1
                                                            3
                                               m =      C . B . A  ,  m =  C . B . A
                                                             7
                                                 4
                   3.21 Finding an  expression  for the        3.21 AmCQ>nwQ> hoVw ì`§OH$ kmV H$aZm
                   output
                      Given the truth table, we can write the ex-  `{X Vm{bH$m Xr JB© hmo Vmo AmCQ>nwQ> hoVw ì`§OH$
                  pression for the output variable. For this pur-  AmgmZr go kmV {H$`m Om gH$Vm h¡Ÿ& BgHo$ {b`o gmao
                  pose, find all the minterms and add logically.  {_ÝQ>_© {ZH$mbH$a CZH$mo Omo‹S>Zm hmoVm h¡Ÿ& AV… AmCQ>nwQ>
                  Thus,  “The output expression is logical sum of  gmao {_ÝQ>_m] H$m Vm{H©$H$ `moJ hmoVm h¡Ÿ& {ZåZ Vm{bH$m H$mo
                  all the minterms.” e.g. Consider the following  XoImo…
                  truth table:
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