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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 (59.6k points) | 927 views

5 Answers

+5 votes
Best answer
  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 equal to $ \bar x.$

Hence, option (D) $ \ X NOR \ 1$ .

answered by Boss (40.6k points)
edited by
0
(3) is calculation is not correct...1+anything =1 ...
0
Updated Thanks!
+13 votes
answer - D

x OR 1 = 1 and so x NOR 1 = 0.
answered by Loyal (9k points)
+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 (45.3k points)
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 (11k points)


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