Minimized expression in SOP form is $f$ = $X+Y'Z$

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+14 votes

Consider the circuit above. Which one of the following options correctly represents $f\left(x,y,z\right)$

- $x\bar{z}+xy+\bar{y}z$
- $x\bar{z}+xy+\overline{yz}$
- $xz+xy+\overline{yz}$
- $xz+x\bar{y}+\bar{y}z$

+31 votes

Best answer

Result of MUX (first one), is,say f1, = xz'+ y'z

Result of MUX(second one , f= f1y' +xy

=(xz'+y'z)y'+xy = xy'z' +y'z +xy =x(y'z' +y) +y'z = x(y'+y)(z'+y) +y'z =xz'+xy+y'z .

Option A.

Note:

1. f =I_{0}S' +I_{1}S ,for 2:1 MUX , where I0 and I1 are inputs , S is select line

2. Distributive property , A+BC = (A+B)(A+C)

3. A+A' =1

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