GATE CSE 2019 | Question: 30

Question

Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as

$f_1=\Sigma(0,2,5,8,14),$

$f_2=\Sigma(2,3,6,8,14,15),$

$f_3=\Sigma (2,7,11,14)$

For the following circuit with one AND gate and one XOR gate the output function $f$ can be expressed as:

• A. $\Sigma(7,8,11)$
• B. $\Sigma (2,7,8,11,14)$
• C. $\Sigma (2,14)$
• D. $\Sigma (0,2,3,5,6,7,8,11,14,15)$

Comments

https://gateoverflow.in/302818/gate-cse-2019-question-30?show=302940#a302940 preferred

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f1​=Σ(0,2,5,8,14)

f2=Σ(2,3,6,8,14,15)

f1 AND f2 = common element = (2,8,14) = f(lets)

f XOR F3 = (2,8,14) xor (2,7,11,14) = (7,8,11)

option A is correct

Answer 1

AND gate takes common form both the terms and xor is inequality detector i .e. it gives output of those terms which are not common in both of the sop. So, answer is A.

Answer 2

Answer is Option A

f1 AND f2 is 1 only when both the inputs are 1, so we need to find the common minterms in both the functions
 

that would be (2,8,14)

now this (2,8,14) along with f3 are given as input to XOR gate , which returns true iff exclusively one input is true

so here we would have to eliminate the common minterms in (2,8,14) and f3

this will give us the answer (7,8,11)