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Functionally complete set is by which you can perform all operations. So, if any logical set is able to implement the operation {And ., NOT} or {OR, NOT} ; it is known as functionally complete .

Now come to NOR gate .

A(NOR)B= (A+B)'

A(NOR)A =(A+A)' =(A)' , so we can perform the NOT operation .

(A+B)' NOR (A+B)' =((A+B)' + (A+B)')' =((A+B)')' =(A+B) , so OR operation is also performed successfully .

So, NOR is the functionally complete .

Now come to NOR gate .

A(NOR)B= (A+B)'

A(NOR)A =(A+A)' =(A)' , so we can perform the NOT operation .

(A+B)' NOR (A+B)' =((A+B)' + (A+B)')' =((A+B)')' =(A+B) , so OR operation is also performed successfully .

So, NOR is the functionally complete .

+1 vote

WE Know that we can derive any GAte from NAND,NOR, so all boolean functions can be derived from NOR

so it is functionally complete

http://www.electrical4u.com/universal-gate-nand-nor-gate-as-universal-gate/

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