Boolean circuit input closed

Question

Comments

Correct me if I'm wrong but D is the only expression that does NOT give the result F=1....

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it is giving $\sum$(1,3,5,7)

option d is correct

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Can you please explain? @joshi_nitish

Answer 1

Only Option(D) matches with this. 

So, correct answer is (D) A=0, B=0, C=1

Comments

Sorry,I have not seen the updated comment that

3 input XNOR behaves same as the complement of 3 input XOR.

For any n input exnor and xor will always be complement.Am it correct?

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I have read that for more than 2-input XNOR gate, if odd no. of inputs are 1, then o/p will be 0, otherwise 1.

In other words, if even no. of inputs are 1 then the output is 1.

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Yeah.Thats correct ,because xor gives high for add number of 1's and so it is odd parity detector so xnor as its complement should give high on even numbers and it is even parity detector.

Answer 2

Detailed Video Solution, with Complete Analysis: https://youtu.be/edSHGdnHBdw  

Let $X = A \oplus B$ ; So, $\overline{X} = A \odot B$

The output $F = \overline{X \oplus \overline{X} \oplus C }$

So, $F = C$

Note that the two of the inputs of the final XNor gate are always opposite($X$, $\overline{X}$), hence, $\mathrm{F} = C.$
Hence, for $F$ to be 1; Inputs $\text{A, B}$ can be anything, But $\text{C}$ must be $1.$

So, answer is Option D. 

& The number of input combinations $\text{(A, B, C)}$ for which the output $\text{F}$ becomes $1$ is $4.$

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NOTE:

3-input XOR function is SAME as 3-input XNOR function.

BUT

3-input XNOR Gate is NOT same 3-input XOR Gate.

Watch this: XNOR Gate Vs XNOR Function | 3 Inputs XNOR gate | GATE EC 2010, GATE EC 2015

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XOR & XNOR functions: https://www.youtube.com/watch?v=-30dUjh6Qv4 

After watching THIS video solution, Solve this GATE EC 2015 question: https://ec.gateoverflow.in/631/gate-ece-2015-set-1-question-38