How to simplify boolean function into two logic gates?


Can anyone help me to simplify this boolean function into two logic gates?

C(out) = AC(in) + BC(in) + AB

Answers:


This expression represents what is commonly known as a three input majority gate - the output is TRUE only when the majority of inputs are true (2 or 3 inputs must be true for the 3 input case). In general it takes 4 basic logic gates to implement this (5 if you you are restricted to 2-input gates).

If you Google for "majority gate" you will find a variety of implementations, e.g. on this page I found the following, which I think matches your criteria (other than the unfeasible requirement of doing it with only 2 gates):

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