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GO Classes DPP | GATE CS | Digital Logic | MUX Implementation

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The function $\mathrm{F}(\mathrm{A},\mathrm{B},\mathrm{C})=\Sigma _m(1,2,5,7)$ is to be implemented using a $4:1$ MUX with select lines $\mathrm{S}_1=\mathrm{A}$ and $\mathrm{S}_0=\mathrm{B}$. 

What should be connected to $\mathrm{I}_0,\mathrm{I}_1,\mathrm{I}_2,\mathrm{I}_3$ respectively?

  1. $\mathrm{C}',\mathrm{C},\mathrm{C},\mathrm{C}'$
     
  2. $\mathrm{C},\mathrm{C},\mathrm{C}',\mathrm{C}$
     
  3. $\mathrm{C},\mathrm{C}',\mathrm{C},\mathrm{C}$
     
  4. $\mathrm{C}',\mathrm{C}',\mathrm{C},\mathrm{C}$

2 Answers

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Since $\mathrm{A}$ and $\mathrm{B}$ are select lines, check the function for each fixed value of $\mathrm{A}\mathrm{B}$.

For $\mathrm{A}\mathrm{B}=00$, possible minterms are $m_0$ and $m_1$.

Only $m_1$ is present, so output is $1$ when $\mathrm{C}=1$.

Therefore, $\mathrm{I}_0=\mathrm{C}$.

For $\mathrm{A}\mathrm{B}=01$, possible minterms are $m_2$ and $m_3$.

Only $m_2$ is present, so output is $1$ when $\mathrm{C}=0$.

Therefore, $\mathrm{I}_1=\mathrm{C}'$.

For $\mathrm{A}\mathrm{B}=10$, possible minterms are $m_4$ and $m_5$.

Only $m_5$ is present, so output is $1$ when $\mathrm{C}=1$.

Therefore, $\mathrm{I}_2=\mathrm{C}$.

For $\mathrm{A}\mathrm{B}=11$, possible minterms are $m_6$ and $m_7$.

Only $m_7$ is present, so output is $1$ when $\mathrm{C}=1$.

Therefore, $\mathrm{I}_3=\mathrm{C}$.

Answer: C

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