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25 votes
25 votes

A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those. Which of the following sets of connectives is NOT functionally complete?

  1. EX-NOR
  2. implication, negation
  3. OR, negation
  4. NAND
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4 Comments

what is the meaning of  functionally complete here ??
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@air1ankit  A  set is FC if you can derive all other operations from that set of operations. (Similar to universal gates).

Eg: {AND, NOT} ~ NAND, {OR, NOT} ~ NOR

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@air1ankit In the answers below we know {and, not}, {or, not} and {and, or, not} are functionally complete set, therefore we are trying to derive these operations from the given operation.

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2 Answers

45 votes
45 votes
Best answer
EX-NOR is not functionally complete.

NOR and NAND are functionally complete logic gates, OR , AND, NOT any logic gate can be implemented using them.

And (Implication, Negation) is also functionally complete

First complement $q$ to get $q'$ then $p \rightarrow q' = p' + q'$

Now complement the result to get AND gate $(p' + q')' \rightarrow pq$
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4 Comments

okay bro then what we should be consider when they asked about functional complete . should it be consider partial functional complete is functional complete?
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In the gate question, if they didn't use the partial functional term, then we can take external input and say it is functionally complete, otherwise they will specify in the questions.
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thank u
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2 votes
2 votes
Option -A)

B) implication,negation is functionally complete because ,

                    f( p , q) = p-->q = !p OR q

                    f( !p , q) = p OR q (since we already have NOT we can use it straightaway) .

C) is functionally complete as it is the basic functionally complete set.

D) NAND is a universal gate which can implement NOT,AND,OR . (or even anyother gates,since it is a universal gate)
Answer:

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