MadeEasy Workbook | MUX

Question

Q. 1 Find the simplified boolean expression $f(x, y, z, w)$ for the below 8 : 1 MUX

• A. $\bar{x} y+x z+\bar{z} w+\bar{y} w$
  
• B. $x \bar{y}+\bar{y} w+\bar{x} z+x z$
  
• C. $\bar{x} y+x z+z \bar{w}+\bar{y} w$
  
• D. $x \bar{y}+x z+z \bar{w}+\bar{y} w$

Comments

option D should be correct

X   Y      Z     W

0    0      0    1

0    0      1    1,0

0    1      0      left

0     1      1     0

1     0      0     1,0

1     0       1    left

1      1      0     1,0

1       1      1    1,0

After this we can make K map

and   simplify and get ans y’w+ xy’+xz+zw’

here from the given option select D ans

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Thank you :)

Answer 1

The given $8:1$ multiplexer output:

$f(x,y,z,w)=\bar x\bar y\bar z I_0+\bar x\bar yzI_1+\bar xy\bar zI_2+\bar xyzI_3+x\bar y\bar zI_4+x\bar yzI_5+xy\bar zI_6+xyzI_7$

$f(x,y,z,w)=\bar x\bar y\bar zw +\bar x\bar yz+\bar xyz\bar w+x\bar y\bar z+x\bar yz++xyz$

$f(x,y,z,w)=\sum(1,2,3,6,8,9,10,11,14,15)$

Solve using k-map we get:

$f(x,y,z,w)=x\bar y+z\bar w+xz+w\bar y$

Option (D) is correct.

Comments

Thank you