Hi everyone,

I've the following problem:

I tried to get the expression of H, which is in sum of products form: A'B'C+A'BC'+A'BC+AB'C+ABC, simplifying it: A'B+C.

I hoped that I get some similarity between H and the given F. I tried to convert both to SOP or POS but couldn't get to anything.


Any hints?

 

F=(A'+B)C
F=A'C+BC
F=A'1C+1BC
F=A'(B+B')C+(A+A')BC
F=A'BC+A'B'C+ABC+A'BC
F=A'BC+A'B'C+ABC

H=A'B'C+A'BC'+A'BC+AB'C+ABC

It would probably be easier now to work from the truth table of H.

 

Another way to look at it might be if you wrote out the truth table for F and compare it to H, you can see there are some inputs that will make F=0 and H=1 - these are where G has to be 1. There are, as suggested in the prompt, possibilities of both F and G being 1.