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I would recommend reading the Circuit Complexity lecture notes by Jonathan Katz, in which he discusses the problem clearly. You start off on the right foot. For two-input, single-output gates, there are 16 different possible logical functions. Each of the two gate inputs can either be from another of the $m$ gates or from one of the $n$ inputs, which leaves ...
What is exactly ur problem? I mean do u need help understanding Karnaugh maps, or expressions reductions??? Karnaugh Maps for O/P one: u draw a table for the i/p values say $AB$ for the rows and $CD$ for the columns, but remember that $11$ precedes $10$ to simplify the reduction. $d$ means $Don't$ $Care$ to use the non existing values to simplify the ...