GATE2006-35

Question

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

• A. $x\bar{z}+xy+\bar{y}z$
• B. $x\bar{z}+xy+\overline{yz}$
• C. $xz+xy+\overline{yz}$
• D. $xz+x\bar{y}+\bar{y}z$

Comments

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

Answer 1

Result of MUX (first one), is, say $f_1 = x\bar z+ \bar yz$
Result of MUX(second one), $f= f_1\bar y +xy$

$\qquad =(x\bar z+\bar yz)\bar y+xy$
$\qquad  = x\bar y\bar z +\bar yz +xy$
$\qquad =x(\bar y\bar z +y) +\bar yz$
$\qquad  = x(\bar y+y)(\bar z+y) +\bar yz$
$\qquad =xz'+xy+y'z .$

Option A.

Note:

1. $f =I_0\bar S +I_1S,$ for $2:1$ MUX, where $I_0$ and $I_1$ are inputs, $S$ is the select line

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

3. $A+\bar A =1$

Answer 2

if you solve this you will get XY' + Y'Z + XY (this can be simplified to X + Y'Z) with min terms as (1,4,5,6,7)

and option A has the same min terms

so option A is equivalent to XY' + Y'Z + XY

Ans (A)

Comments

need correction ...

its xy+xz'+y'z