The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+8 votes
798 views

Which of the following expressions is not equivalent to $\bar{x}$?

  1. $x \text{ NAND } x$
  2. $x \text{ NOR } x$
  3. $x \text{ NAND } 1$
  4. $x \text{ NOR } 1$
asked in Digital Logic by Veteran (59.4k points) | 798 views

5 Answers

+13 votes
Best answer
answer - D

x OR 1 = 1 and so x NOR 1 = 0.
answered by Loyal (9.2k points)
selected by
+5 votes

x NAND x

Lets do it for AND first  

 x AND x = x (Idempotent property)  Now take negation on both side  ____   __ 

                                                                                                      x.x =  x

x NOR x 

Lets do it for OR first  

 x OR x =x (Idempotent property) Now take negation on both side   _____     ___

                                                                                                  x + x   =    x

x NAND 1 

Again do it for AND first    x AND 1 = x Take negation on both side   ____    __

                                                                                                    x .1 =  x

x NOR 1

Do it for OR first        

 x OR 1 = 1   Noe negate on both side    ______     __

                                                             x + 1   =  1     = 0

So answer is D.

NOTE - Line (---------     ----)  are representing negation  

answered by Boss (45.1k points)
+3 votes
(1) $\overline {X X}= \bar X$

(2)$\overline {X+X}= \bar X . \bar X =\bar X$

(3)$\overline {X .1 }= \bar X + 0= \bar X$

(4)$\overline {X +1}= \bar X. 0 = 0$

 $Here \ X \ NOR \ 1 \ will \ not\ be \ equals \ to \ \bar x$

 
Hence,Option(4)$\ X \ NOR \ 1$ .
answered by Boss (39.6k points)
edited by
0
(3) is calculation is not correct...1+anything =1 ...
0
Updated Thanks!
0 votes
D), as X nor 1 will always be 0, irrespective of state of X
answered by (169 points)
0 votes
x nor x means complement of (x+x) that is x's complement so equal, only d differs as it evaluates to 0
answered by Boss (10.9k points)


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

35,507 questions
42,829 answers
121,693 comments
42,183 users