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UGC NET Computer Science Nov 2020 (Paper II)

Simplified expression/s for following Boolean function

$F(A,B,C,D)=\sum(0,1,2,3,6,12,13,14,15)$

is/are

(A) $A'B' + AB + A'C'D'$

(B) $A'B' + AB + A'CD'$

(C) $A'B' + AB + BC'D'$

(D) $A'B' + AB + BCD'$

Choose the correct answer from the options given below:

Solution

Given minterms are:

$0,1,2,3,6,12,13,14,15$

$A'B'$ covers minterms $0,1,2,3$

$AB$ covers minterms $12,13,14,15$

Remaining minterm is $6$

Option (B):

$A'CD'$ covers minterms $2,6$

Both are present in the function.

So, option (B) is correct.

Option (D):

$BCD'$ covers minterms $6,14$

Both are present in the function.

So, option (D) is also correct.

Options (A) and (C) include minterm $4$, which is not present in the function.

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