The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+18 votes
1.1k views

A Boolean function $x’y’ + xy + x’y$ is equivalent to

  1. $x' + y'$
  2. $x + y$
  3. $x + y'$
  4. $x' + y$
asked in Digital Logic by Veteran (59.7k points) | 1.1k views

4 Answers

+17 votes
Best answer

Answer is option D.

$x'y' + x'y = x'(y+y') = x'$
$x' + xy = x' + y$

answered by Veteran (367k points)
edited by
0
how x' + xy = x' + y ????
0
x' + xy = x'(y+y') + xy

           =x'y + x'y' + xy

           =x'y + x'y + x'y' + xy                   (because AB+AB+AB+.......................=AB)

           =(x'y + x'y') + (x'y + xy)

           =x'(y+y') + y(x+x')

           =x'+y
0

@lash12

how x' + xy = x' + y ????

     $x' + x.y$   [ In this case $+$ is distributed over $.$  (In boolean algebra this is also possible.]

       $x' + x.y=(x'+x).(x'+y)$

       $x' + x.y=(1).(x'+y)$         $ [\bar{A}+A=1]$

       $x' + x.y=(x'+y)= x'+y$ 

+9 votes
answer - D

use K map
answered by Loyal (8.9k points)
0
Use distribution rule  ...
+3 votes
= X'Y' + XY +X'Y

= X' ( Y + Y' ) + Y ( X + X')

= X' + Y

hence option d is correct
answered by Active (4.1k points)
+1 vote

Using K map for two variables

  y' y
x' 1 1
x 0 1

Tables for expression given looks like this from this we get:

x'+y 

 

answered by (77 points)
Answer:

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

44,200 questions
49,671 answers
163,564 comments
65,819 users