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38 votes
What is the minimum number of $2$-input NOR gates required to implement a $4$ -variable function expressed in sum-of-minterms form as $f=\Sigma(0,2,5,7, 8, 10, 13, 15)?$ Assume that all the inputs and their complements are available. Answer: _______
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Best answer
46 votes
46 votes

$f = ( B' + D ) . ( B + D' )$

It is mentioned that both Complimentary as well as Uncomplimentary forms are available.

$B'\text{ NOR }D = (B' + D)'$

$B \text{ NOR } D' = (B + D')'$

$(B' \text{ NOR } D) \text{ NOR } (B \text{ NOR } D')$

$= ( (B' + D)' + (B + D')' )'$

$= ( (B' + D)'' . (B + D')'' )$

$= ((B' + D).(B + D'))$

$= f$

Thus, $3 \text{ NOR }$ Gates are required.

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55 votes
55 votes

$3$ NOR GATE is required.

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20 votes
20 votes

Using K-map method we can reduce this to xnor and to implement xnor we will only need 3 nor gates if both inputs and their complements are available.

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15 votes
15 votes

I THINK ANSWER IS 4 ! PLEASE CHECK THIS PIC 

Answer:

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