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

The Gateway to Computer Science Excellence

First time here? Checkout the FAQ!

x

+15 votes

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

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

+32 votes

Best answer

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. $A+\bar A =1$

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. $A+\bar A =1$

- All categories
- General Aptitude 1.3k
- Engineering Mathematics 5.4k
- Digital Logic 2.1k
- Programming & DS 4k
- Algorithms 3.4k
- Theory of Computation 4.2k
- Compiler Design 1.6k
- Databases 3.1k
- CO & Architecture 2.7k
- Computer Networks 3.1k
- Non GATE 1.1k
- Others 1.4k
- Admissions 501
- Exam Queries 449
- Tier 1 Placement Questions 19
- Job Queries 62
- Projects 12

38,058 questions

45,554 answers

131,898 comments

48,916 users