Page 211 - FUNDAMENTALS OF COMPUTER

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NPP Number System, Boolean Algebra and Logic Circuits 211

Writing the terms for each group (Solving g_yhm| Ho$ {b`o nX {bIZm (1 H$s ghm¶Vm go hb)
with 1)
Once we have formed groups of 1 we can 1 Ho$ g_yh ~ZmZo Ho$ níMmV² SOP ê$n _| gab
S
write simplified expression in SOP form with ì`O§H$ Bg àH$ma {ZH$mbm Om gH$Vm h¡:
the following steps:
1. Move top to bottom, left to right in a group. 1. {H$gr g_yh _| D$na go ZrMo d ~mE± go XmE± MbZo
Eliminate the variables which are changing. na Omo Ma n[ad{V©V hmoVo h¢, CÝh| hQ>m Xmo &
2. If a variable is constant at zero, write 2. `{X EH$ Ma 1 na {Z`V h¡ Vmo Bgo d¡go hr {bImoŸ&
complement of it else write the uncomple- O¡go A = 1 h¡ Vmo A {bImoŸ&
mented variable. e.g. If A = 1 write A else write
A
3. Put dot in between all the variables 3. `{X H$moB© Ma 0 na {Z`V h¡ Vmo CgH$m H$m°påßb_|Q>
obtained in step 2. {bImoŸ& O¡go A = 0 h¡ Vmo A {bImoŸ&
4. Apply step 1 to 3 for all the groups and 4. H«§$. 2 d 3 go Omo Ma {_bo CZHo$ ~rM _o §S>m°Q>
take logical sum of all the terms obtained. bJmAmoŸ& H«§$. 1 go 3 g^r g_yhm| Ho$ {bE XmohamAmo
The simplified expression; in SOP form VWm g^r nXm| H$m `moJ bmoŸ& ¶hr gab ì¶O§H$ h¡&
will be obtained:
Solving with Zeros ‘0’ eyÝ` H$s ghm`Vm go hb
If we make group of zeros, we get POS `{X h_ eyÝ` H$s ghm`Vm go g_yh ~ZmVo h¢ Vmo h_|
form of simplified expression. Following steps POS ê$n _| hb {_boJm Ÿ& eyÝ` go hb H$aZo hoVw {ZåZ
are involved while solving with zeros: H$m`© H$aZo hm|Jo…
1. Move downward and left to right in a 1. {H$gr ^r g_yh _| D$na go ZrMo d ~mE§ go XmE§ OmAmo&
group of zero, eliminate those variables Omo Ma n[ad{V©V hmo aho h¢ CÝh| N>mo‹S> Xmo Ÿ&
which change.
2. If a variable is constant at zero do not 2. `{X H$moB© Ma 0 na {Z`V h¡ Vmo Cgo Eogo hr {bI
complement it. else take complement. Xmo O¡go `{X A = 0 Vmo A {bImo AÝ`Wm A {bImoŸ&
3. Put logical plus between all the variable 3. H«§$. 2 go àmá g^r Mam| Ho$ ~rM (+) H$m {MÝh
formed in step 2. bJmAmo&

4. Take logical product of all the terms 4. Bgr Vah àË`oH$ g_yh Ho$ {bE 1 go 3 XmohamAmo&
obtained for each group. We get simplified àmá g^r nXm| H$m Vm{H©$H$ JwUm H$amo & `hr POS
expression in POS form. ê$n _| gab ì`§OH$ h¡Ÿ&