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NIMCET 2015 — Computer PYQ

NIMCET | Computer | 2015

The minimum number NAND gates required to realize $AB + AB'C + AB'C'$ is

Choose the correct answer:

A.
3
B.
2
C.
1
D.
0
(Correct Answer)

Explanation

Step 1: Simplify the expression

The given expression is:

$F = AB + AB'C + AB'C'$

First, take $AB'$ as a common factor from the last two terms:

$F = AB + AB'(C + C')$

We know that according to the Complement Law, $C + C' = 1$ :

$F = AB + AB'(1)$

$F = AB + AB'$

Now, take $A$ as a common factor:

$F = A(B + B')$

Again, using the Complement Law ( $B + B' = 1$ ):

$F = A(1)$

$F = A$

Step 2: Determine the number of gates

The simplified expression is $F = A$ . This means the output is directly equal to the input $A$ .

Since the output is just a direct connection to the input variable $A$ , no logic gates are required to realize this function.

Conclusion:

The minimum number of NAND gates required is 0.

The correct option is (d).