GATE IT 2007 | Question: 8

Question

The following circuit implements a two-input AND gate using two $2-1$ multiplexers.

What are the values of $X_1, X_2, X_3$?

• A. $X_1 = b, X_2 = 0, X_3 = a$
• B. $X_1 = b, X_2 = 1, X_3 = b$
• C. $X_1 = a, X_2 = b, X_3 = 1$
• D. $X_1 = a, X_2 = 0, X_3 = b$

Comments

@GateCse

why a,b is considered as a.b not (a+b)

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if we put the value on expression $F(a,b)=\bar{X_3.}X_2+X_3(\bar X_1.b+X_1.a)$

option 1) : $ab$

option 2): $a+\bar b$

option 3): $a+b$

option 4): $b$

Answer 1

Answer: A

$F = (bX_1' + aX_1)X_3 + X_2X_3'$

Put $X_1 = b, X_2 = 0, X_3 = a$ to get $F = ab.$

Comments

+1 Thank You!

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If in option B if X2 was 0 then B also could have been right?

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Right pepper

Answer 2

F = (bX1' + aX1)X3 + X2X3'
If we put
X1 = b
X2 = 0
X3 = a
Then we get,
F = ab