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GO Classes DPP | GATE CS | Digital Logic | K-map Simplification

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For the Boolean function $\mathrm{F}(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D})=\Sigma _m(0,4,5,6,7,8,9)$, which of the following is the minimal POS form using K-map?

  1. $\mathrm{F}=(\mathrm{A}'+\mathrm{B}')(\mathrm{B}+\mathrm{C}')(\mathrm{A}+\mathrm{B}+\mathrm{D}')$
     
  2. $\mathrm{F}=(\mathrm{A}+\mathrm{B})(\mathrm{B}+\mathrm{C}')(\mathrm{A}'+\mathrm{B}'+\mathrm{D})$
     
  3. $\mathrm{F}=(\mathrm{A}'+\mathrm{B}')(\mathrm{B}'+\mathrm{C})(\mathrm{A}+\mathrm{B}+\mathrm{D}')$
     
  4. $\mathrm{F}=(\mathrm{A}'+\mathrm{B}')(\mathrm{B}+\mathrm{C})(\mathrm{A}+\mathrm{B}+\mathrm{D})$

3 Answers

0 0 votes

Given $\mathrm{F}(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D})=\Sigma \mathrm{m}(0,4,5,6,7,8,9)$.

For POS simplification, we group the $0$s in the K-map.

The $0$s are at $m_1,m_2,m_3,m_{10},m_{11},m_{12},m_{13},m_{14},m_{15}$.

 

 

Final Answer: A

0 0 votes
Loop from 0 to 15 then check number which is  not present in sop representation  (1,2,3,10,11,12,13,14,15) .

Now apply  rule we get 2 quad , 1 pair

so option A is correct.
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