Page 194 - FUNDAMENTALS OF COMPUTER

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194 Fundamentals of Computers NPP

Bubbled AND and NOT Gates can be ~~ëS> AND VWm NOT JoQ> H$mo NOR H$s ghm`Vm
replaced by NOR: go ~ZmZo na:

A

B
Y

3.18 Representation of Boolean Ex- 3.18 ~y{b`Z ì`§OH$ H$m à{V{Z{YËd
pression
Any Boolean expression can be repre- {H$gr ^r ~y{b`Z ì`§OH$ H$mo Xmo àH$ma go {bIm
sented in two ways: Om gH$Vm h¡ …

1. SOP (Sum Of Products) Form. 1. SOP (g_ Am°\$ àmoS>ŠQ>)
2. POS (Product Of Sum) Form. 2. POS (àmoS>ŠQ> Am°\$ g_)
Consider one by one. A~ h_ BÝh| EH$-EH$ H$aHo$ XoIVo h¢ …
1. SOP Form: 1. SOP JwUZ\$bm| H$m `moJ
Consider the given expression: {ZåZ ì`§OH$ H$mo XoImo…

F = B . A + D . C
F is a Boolean function which is summa- F EH$ Eogm ì`§OH$ h¡ Omo Xmo JwUZ\$bm| .A B VWm
tion of two products A B . and C.D. Other ex- C.D H$m `moJ h¡Ÿ& Bgr àH$ma {ZåZ CXmhaU SOP H$mo
amples of SOP form are: Xem©Vo h¢…
Y = C . B . A + C . B . A + C . B . A

Q = D . C . B . A + D . C . B . A + D . C . B . A
F = Z . Y . X + Z . Y . X
A canonical SOP form is that in which all EH$ Ho$Zmo{ZH$b SOP \$m°_© dh hmoVr h¡, {Og_| gmao
the products contain equal number of variables: nXm| _| g_mZ g§»`m _| Ma am{e`m± hmoVr h¢Ÿ& O¡go,
e.g. A C . B . + C . B . A + C . B . A is canonical SOP C . B . A + C . B . A + C . B . A EH$ Ho$Zmo{ZH$b ê$n h¡ naÝVw
form. But the following expression is not:
{ZåZ Zht…

D . C . B . A + D . C . B . A + ABC . This is called D . C . B . A + D . C . B . A + ABC `h ñQ>¢§S>S>© \$m°_©
standard form. H$hcmVm h¡Ÿ&

2. POS form 2. POS (`moJm| H$m JwUZ\$b)
Consider the given expression: {ZåZ ì`§OH$ Xo{I`o:
F = (A + B ) (A. + B )