UGC NET CSE | October 2020 | Part 2 | Question: 42

Question

Simplified expression/s for following Boolean function

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

1. $A’B’+AB+A’C’D’$
2. $A’B’+AB+A’CD’$
3. $A’B’+AB+BC’D’$
4. $A’B’+AB+BCD’$

Choose the correct answer from the options given below:

• A. $(i)$ only
• B. $(ii)$ only
• C. $(i)$ and $(ii)$ only
• D. $(ii)$ and $(iv)$ only

 

Answer 1

 

 

hence option D is correct ans

Answer 2

Correct Answer : D

	C'D'	C'D	CD	CD'
A'B'	1	1	1	1
A'B				1
AB	1	1	1	1
AB'

Equivalent Expressions :

1) A'B' + AB + A'CD'

2) A'B' + AB + BCD'

Both b and d are equivalent. Hence Ans is Option D)

 

 

Answer 3

The given boolean function can be solved using 4 variable k-map.

In above k-map minterm $(m_0,m_1,m_2,m_3)$ & $(m_{12},m_{13},m_{14},m_{15})$ are essential but for minterm $m_6$ we have $2$ choices; $(m_2,m_6)$ or $(m_{14},m_6)$

So expression are:

1. $A’B’+AB+BCD’$
2. $A’B’+AB+A’CD’$

So option $(D)$ is correct.

Answer 4

 

 

ANS : D 

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

EQUIVALENT EXPRESSION : 

A'B' + AB + A'CD'  AND 

 A'B' + AB + BCD' HENCE OPTION B AND D ARE CORRECT