ISRO ECE 2016 | combinational logic

Question

 

in given combinational logic $X=?$

1. $X = AB'C' +A'BC'+ A'B'C+ ABC$
2. $X = A'BC +A'BC'+ AB'C+ A'B'C'$
3. $X = AB + BC + AC$
4. $X= A'B'+B'C'+A'C'$

Comments

https://gateoverflow.in/?qa=blob&qa_blobid=18425009085999919061

Answer 1

The output expression of 1st multiplexer is:

$ Y=\bar A\bar BI_0+\bar A BI_1+ A\bar BI_2+ A BI_3$

$Y=\bar A\bar B.0+\bar A B.1+ A\bar B.1+ A B.0$

$Y=\bar A B+ A\bar B= A\oplus B$

The output expression of 2nd multiplexer is:

$X=\bar Y\bar CI_0+\bar Y CI_1+ Y\bar CI_2+ YCI_3$

$X=\bar Y\bar C.0+\bar Y C.1+ Y\bar C.1+ YC.0$

$X=\bar Y C+ Y\bar C$

$X=(\overline{A\oplus B}) C+ (A\oplus B)\bar C$

$X=(\bar A\bar B+AB)C+(\bar AB+A\bar B) \bar C$

$X=\bar A\bar BC+ABC+\bar AB\bar C+A\bar B\bar C$

Option $(B)$ is correct.

Comments

There is a typo I think, you solved it correctly and the answer matches with option (A), but in the last line you write option (B).

Please do this small update, and if missed something then please enlighten me.

Answer 2

it gives a xor b xor c as output
now a exor b exor c is 1 iff number of 1 are odd
so when number of 1 is 1 and 3 it gives us our answer
option A follows the same condition