Page 224 - FUNDAMENTALS OF COMPUTER

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224 Fundamentals of Computers NPP

A B C 00 01 11 10

0 0 0 0 0

1 0 1 1 1

Now the uncovered one can be overlapped A~ EH$ ~Mm hþAm 1 VWm EH$ noAa Ho$ 1 H$mo
to give on more pair. (do not make a single) Amodabon H$aHo$ EH$ Am¡a noAa ~ZoJm Ÿ& (AJa qgJb ~Zm

X|Jo Vmo JbV hmoJm)Ÿ&
A B C 00 01 11 10

0 0 0 0 0

1 0 1 1 1

We have two pairs in the Karnaugh map. H$aZm°\$ _¡n _| Xmo no`g© hmoVo h¢Ÿ& XmoZm| no`g© EH$
Both pairs overlap. Therefore this technique is Xygao H$mo Amodabon H$aVo h¢Ÿ& AV: Bg VH$ZrH$ H$mo g_yhm|
called overlapping of the groups.
H$s AmodaboqnJ H$hm OmVm h¡Ÿ&
Now we have to obtain the terms for both A~ h_| XmoZm| no`g© Ho$ {bE nX àmßV H$aZm h¡Ÿ& ~m§`o
the pairs. Consider left pair. Go from top to bot- no`a na {dMma H$a|Ÿ& D$na go ZrMo Om`| VWm ~m§`o go Xm§`o,
tom and left to right, here B changes from 0 to `hm§ B H$m _mZ 0 go 1 VH$ ~XbVm h¡Ÿ& Bg àH$ma B H$mo
1. Thus, eliminate B. A is constant at 1 therefore hQ>m X|Ÿ& A H$m _mZ 1 na pñWa h¡ AV: A {bI|Ÿ& C ^r 1
write A.C is also fixed at 1. Therefore write C. na {ZpíMV h¡Ÿ& AV: C {bI|Ÿ&
We have the term for this pair: AV… A .C Bg noAa hoVw nX h¡:
A.C
Similarly for right pair, A is fixed at 1 and Bgr àH$ma Xm§`o no`a Ho$ {bE A H$mo 1 na {Z`V {H$`m
B is fixed at 1. C changes, therefore remove C.
The term is A.B. OmVm h¡ VWm B H$mo 1 na {Z`V {H$`m OmVm h¡, C _|
n[adV©Z hmoVm h¡, AV: C H$mo hQ>m X|Ÿ& nX H$m _mZ A.B. h¡Ÿ&

Therefore the simplified expression is sum Cnamoº$ XmoZm| nXm| H$m `moJ boZo na gab ì`§OH$
of these terms: àmßV hmoJm…
F = A.C + A.B
(c) The given equation is: (c) {X`m J`m ì`§OH$ h¡:
Y = D . C . B . A + D . C . B . A + D . C . B . A