Modern Physics 6 Question 10

10. The output of the given logic circuit is

(Main 2019, 12 Jan I)

(a) AB¯

(b) A¯B

(c) AB+AB

(d) AB¯+A¯B

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Solution:

  1. Truth table for given circuit is

A B Y1 Y2 Y3 Y
0 0 1 1 1 0
1 0 1 1 0 1
0 1 1 1 1 0
1 1 0 1 1 0

This is the same output produced by AB¯ gate or

So, given circuit is equivalent to Boolean expression AB¯.

Alternate Method

Using the Boolean algebra, output of the given logic circuit can be given as

Here

Y2=A(AB)

Using de-Morgan’s principle,

xy=x¯+y¯ and x+y=x¯y¯Y2=A¯+(AB)=A¯+(A.B)[x¯=x]Y3=1 As, Y=Y2Y3

Using Eqs. (i) and (ii), we get

Y=(A¯+AB)(1)=(A¯+AB)+1=A¯(AB)+0=A(A¯+B¯)[x+0=x]=AA¯+AB¯[xx¯=0]=AB¯



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