GATE ECE 2010 | Question: 39

Question

The Boolean function realized by the logic circuit shown is

• A. $\text{F} = \sum_{\text{m}} (0, 1, 3, 5, 9, 10, 14)$
• B. $\text{F}=\sum_{\text{m}}(2,3,5,7,8,12,13)$
• C. $\text{F}=\sum_{\text{m}}(1,2,4,5,11, 14,15)$
• D. $\text{F}= \sum_{\text{m}}(2,3,5,7,8,9,12)$

Answer 1

Detailed Video Solution: https://youtu.be/6cP7omPN4qQ 

We can easily solve it by considering cases:

Case 1: When $A= 0, B = 0$

In this case, $f(A,B,C,D) = C$

So, $f = 1$ for the following input combinations: $(A,B,C,D) = (0,0,1,0), (0,0,1,1)$ i.e. $f(A,B,C,D)=1$ for minterms $m_2, m_3.$

Hence, Options $A,C$ are eliminated. 

Now, in the remaining two options, we consider whether $f(A,B,C,D)$ is $1$ or not, for minterm $m_9.$

So, consider case 2: When $A= 1, B = 0$

In this case, $f(A,B,C,D) = \overline{C}$

So, $f = 1$ for the following input combinations: $(A,B,C,D) = (1,0,0,0), (1,0,0,1)$ i.e. $f(A,B,C,D)=1$ for minterms $m_8, m_9.$

Hence, Option $B$ is also eliminated. 

Final answer is Option D.

Detailed Video Solution: https://youtu.be/6cP7omPN4qQ