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I want to know is there any standard way to find out number of NAND gates required to build the circuit. For example in this question:

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My Answer is

In Question they have asked to find no. of nand gates so get sop form of that function and have nand gates at last nand gate replace it with or gate representation of nand gate

If No. of Nor gates are asked then get pos form of function and have all nor gates replace last nor gate with and representation of nor gate

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After solving K-map We get the Output - 

F= (z+w)(x'+y') => z(x'+y') + w(x'+y')

now taking Complement both side-

F' =  ( z(x'+y') + w(x'+y') )'

F' = ( z(x'+y') )' . (w(x'+y') )'

again taking complement -

F =  [ ( z(x'+y') )' . (w(x'+y') )' ]'                     we can also replace  X' + Y' = (XY)'

This can be implemented using 4 NAND gates i.e given circuit in the solution above.

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