GATE CSE 2002 | Question: 2-1

Question

Consider the following logic circuit whose inputs are functions $f_1, f_2, f_3$ and output is $f$

Given that

• $f_1(x,y,z) = \Sigma (0,1,3,5)$
• $f_2(x,y,z) = \Sigma (6,7),$ and
• $f(x,y,z) = \Sigma (1,4,5).$

$f_3$ is 

• A. $\Sigma (1,4,5)$
• B. $\Sigma (6,7)$
• C. $\Sigma (0,1,3,5)$
• D. None of the above

Comments

Option A is right choice for F3

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easy  question

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f1 nand f2 = Σ(0,1,2,3,4,5,6,7)

Answer 1

$f = ((f_1f_2)'f_3')' = f_1f_2 + f_3$

In minimum sum of products form, AND of two expressions will contain the common terms. Since $f_1$ and $f_2$ don't have any common term, $f_1f_2$ is $0$ and hence $f = f_3 =Σ(1, 4, 5).$

Correct Answer: $A$

Comments

if you read the question clearly  then your doubt is clear ....

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Here, nothing is common between $f_{1}$ & $f_{2}$.

• $f_{1}(x, y, z) = Σ(0, 1, 3, 5)$
• $f_{2}(x, y, z) = Σ(6, 7)$ 

 

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made easy guide has a lot of typo that's why people ask such doubts. But even if 5 was common then also 5 + 1,4,5 would have given 1,4 and 5 only...

Answer 2

Here we have NAND - NAND Circuit, we can convert it to following AND - OR circuit. (As NAND is bubbled OR). Now it is easy to solve this question. F1 AND F2 = 0. SO whatever f3 is directly passed to output. So answer is A.

Comments

sir how you convert NAND to AND and NOR to OR ..?

i got you answer but just only wants to know the hidden concept behind the your concept

and i think you should edit your answer "Here we have NAND - NAND Circuit to Here we have NAND - NOR Circuit"

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Here we don't have any nor gate its nand - nand realization which is equivalent to and-or realization.

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this should be the best answer

Answer 3

AND of two minterm expression gives common terms.

$f1\ AND\ f2\equiv f1\cap f2.$

So, $f1\ NAND\ f2\equiv$${(f1\cap f2)'}$

$f1\cap f2=\{0,1,3,5\}\cap\{6,7\}=\phi$ 

And, we have,

$f=[(f1\cap f2)' \cap (f3)']'=f1 \cap f2 \bigcup f3 = \{1,4,5\}$

But, $f1 \cap f2 = \phi$

$\Rightarrow \phi\ U  f3 = \{1,4,5\}$

$ \Rightarrow f3 =\{1,4,5\}$

So, Correct Answer is (A).

Answer 4

ANS ) A

Comments

This is time saving and best answer.