Page 203 - FUNDAMENTALS OF COMPUTER

NPP

NPP Number System, Boolean Algebra and Logic Circuits 203

A B Y
0 0 1
0 1 0
1 0 1
1 1 0
There are two 0s in the output. The first ‘0’ AmCQ>nwQ> _| Xmo ñWmZm| na 0 h¡ Ÿ& nhbm ‘0’ H$m
corresponds to (01) therefore the fundamental
gå~ÝY (01) go h¡ AV: \$ÊS>m_|Q>b g_ (A + B ) h¡Ÿ&
sum is (A + B ). Similarly, for the second ‘0’ the
Bgr àH$ma Xygam ‘0’ Ho$ {bE \$ÊS>m_|Q>b g_ _| Xmo _¡ŠgQ>åg©
fundamental sum is (A + B ), Therefore the ex- (A + B ) VWm (A + B ) hm|JoŸ&
pression for Y will have two maxterms (A + B )

and (A + B ).
Maxterms are represented by M Where n _oŠgQ>_© H$mo M Ho$ ê$n _| Xem©Vo h¢ Ohm± n ~mBZar
n
n
is the decimal equivalent of the corresponding g§»`m H$m Xe_bd Vwë` h¡ Ÿ& Cnamo³V CXmhaU ‘| nhbr
binary number. In the above example the first
binary value is the (01), thus the maxterm is M . ~m¶Zar d¡ë¶y (01) h¡ AV ‘¡³gQ>‘© M h¡& Xÿgar ~m¶Zar
1
1
For the second binary value (11) the maxterm is d¡ë¶y (11) h¡ AV… ‘¡³gQ>‘© M h¡& AV… Cnamoº$ Xmo
3
M . The above representation leads to the fol- _oŠgQ>_m] H$mo Bg àH$ma {bIm Om gH$Vm h¡…
3
lowing equations:
M = (A + B ) and M = (A + B )
3
1
Problem 3.55 àíZ 3.55
For the given Truth Table identify all the {ZåZ _| gmar _oŠgQ>_²©g nhMmZmo…
maxterms:
A B C Z
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Solution: hc:
There are three 0s in the output therefore VrZ eyÝ` Ho$ gmnoj VrZ _oŠgQ>_²©g Bg àH$ma h¢…
three Maxterms will be there. These are listed
below:
M = (A + B + C ), M = (A + B + C )
1
3
and M = (A + B + C )
7