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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:

  1. $(i)$ only
  2. $(ii)$ only
  3. $(i)$ and $(ii)$ only
  4. $(ii)$ and $(iv)$ only

 

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4 Answers

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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)

 

 

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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.

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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 

Answer:

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