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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 | 979 views

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 (40.7k points)
edited
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(3) is calculation is not correct...1+anything =1 ...
0
Updated Thanks!

x OR 1 = 1 and so x NOR 1 = 0.
answered by Loyal (8.9k points)

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 (45.4k points)
D), as X nor 1 will always be 0, irrespective of state of X
answered by (169 points)
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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