NIMCET 2009 Question Paper with solutions

Question : 100 of 120

Marks: +1, -0

The switching expression corresponding to

f(A, B, C, D)

=\sum(1,4,5,9,11,12)

$B\ov{CD}+\ov {AC}D + A\ov{B}D$
$AB\ov{C}+ {ACD}+\ov{ {BCD}}$
$AC\ov{D}+\ov{A} B\ov{ C}- A\ov{CD}$
$\ov{ {A}} {BD}+ AC\ov{D}+ BC\ov{D}$

Validate

Solution:

For the blue group
C and D maintain the same state but A and B change.
Cis zero (0) and has to be negated before it can be included. Thus, the first term is

\ov{ABC}D+\ov{A}B\ov{C}D=\ov{AC}D(B+\ov{B})=\ov{AC}D

For she green group
Second term is

\ov{A}B\ov{CD}+AB\ov{CD}=(A+\ov{A})B\ov{CD}=B\ov{CD}

Forthe red group
The third term

A\ov{BC}D+A\ov{B}CD=A\ov{B}D(C+\ov{C})=A\ov{B}D

∵ f(A,B,C,D)=\ov{AC}D+B\ov{CD}+A\ov{B}C

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