8" X 12" Beam

[littledog]

I changed the dimensions of the 20'x30' 1 1/2 storey house to 22'x32'.  We are doing double 2X4 construction and I enlarged things so that the interior space would not be changed so much.  So I added a beam down the center and two posts to carry it.  The span is around 10' and 11' with the joists framed to the center beam.  I am planning on having it all exposed and use the plank and beam floor above.  My question is how do I size the center beam?  I was given a size of 8"x12" by someone and wondered if that is arbitrary or is that the size it will have to be?  And if the center beam is 8x12 then what do the floor joists need to be (4ft on center or less).  I may be able to mill them myself and just need to know so that I can determine if the logs I have are big enough.  Anyway I would appreciate any input.  Thanks Aaron (aka littledog).