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

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4 4 votes

A $4:1$ MUX has select lines $\mathrm{S}_1=\mathrm{R}$ and $\mathrm{S}_0=\mathrm{S}$, where $\mathrm{R}$ is MSB and $\mathrm{S}$ is LSB. The data inputs are $\mathrm{I}_0=\mathrm{P}$, $\mathrm{I}_1=\mathrm{Q}$, $\mathrm{I}_2=\mathrm{P}'$, and $\mathrm{I}_3=\mathrm{Q}'$.
What is the output $\mathrm{Z}$?

  1. $\mathrm{Z}=\mathrm{R}'\mathrm{S}'\mathrm{P}+\mathrm{R}'\mathrm{S}\mathrm{Q}'+\mathrm{R}\mathrm{S}'\mathrm{P}'+\mathrm{R}\mathrm{S}\mathrm{Q}$
     
  2. $\mathrm{Z}=\mathrm{R}'\mathrm{S}\mathrm{P}+\mathrm{R}'\mathrm{S}'\mathrm{Q}+\mathrm{R}\mathrm{S}'\mathrm{P}'+\mathrm{R}\mathrm{S}\mathrm{Q}'$
     
  3. $\mathrm{Z}=\mathrm{R}'\mathrm{S}'\mathrm{P}'+\mathrm{R}'\mathrm{S}\mathrm{Q}+\mathrm{R}\mathrm{S}'\mathrm{P}+\mathrm{R}\mathrm{S}\mathrm{Q}'$
     
  4. $\mathrm{Z}=\mathrm{R}'\mathrm{S}'\mathrm{P}+\mathrm{R}'\mathrm{S}\mathrm{Q}+\mathrm{R}\mathrm{S}'\mathrm{P}'+\mathrm{R}\mathrm{S}\mathrm{Q}'$

1 Answer

2 2 votes

For a $4:1$ MUX,

$\mathrm{Z}=\mathrm{R}'\mathrm{S}'\mathrm{I}_0+\mathrm{R}'\mathrm{S}\mathrm{I}_1+\mathrm{R}\mathrm{S}'\mathrm{I}_2+\mathrm{R}\mathrm{S}\mathrm{I}_3$

Substitute the given inputs.

$\boxed{\mathrm{Z}=\mathrm{R}'\mathrm{S}'\mathrm{P}+\mathrm{R}'\mathrm{S}\mathrm{Q}+\mathrm{R}\mathrm{S}'\mathrm{P}'+\mathrm{R}\mathrm{S}\mathrm{Q}'}$

Answer: D

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