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

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For the Boolean function $\mathrm{F}(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D})=\Pi _M(3,6,7,12,14)$, which of the following is a correct minimal POS form using K-map?

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

4 Answers

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Given $\mathrm{F}(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D})=\Pi _M(3,6,7,12,14)$.

Since maxterms are given, these are the cells where $\mathrm{F}=0$.

So, place $0$s at $\mathrm{m}_3,\mathrm{m}6,\mathrm{m}7,\mathrm{m}{12},\mathrm{m}{14}$.

 

Answer: C

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if this questionis MSQ  then one more answer along with option C is : (A'+ B '+ D)(A+ C' + D') (A + B' + C') .
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