Problem finding SOP form of f + g

Question

I have a project and I am asked to find the sop form of f+g and find its cost and then compare it to the cost if I implement f and g separately.

I am trying to find SOP form of f+g and I am stack because f and g has nothing in common based on the form of and g that I've found:

f = x2'x5 + x1'x2'x4' + x2x4x5'

g = x1'x2' + x2x3' + x1x2x5

And based on those f+g = x2'x5 + x1'x2'x4' + x2x4x5' + x1'x2' + x2x3' + x1x2x5

Here are my karnaugh maps, f above, g below.

My question is: Should I keep what I have done? Or should I find new forms for f and g so that I can get a form for f + g that makes more sense?

Any tip or answer or any suggestion for my question is welcome. Thanks in advance.

Answer 1

The following three-valued $\{0, 1, X\}$ disjunctive truth table combines two inputs to one output:

f g | f+g
----+----
0 0 |  0
0 1 |  1
0 X |  X
1 0 |  1
1 1 |  1
1 X |  1
X 0 |  X
X 1 |  1
X X |  X

Whenever at least one input is $true$, the output becomes $true$. Both inputs have to be $false$ to make the output $false$. Input combination of $false$ and don't care leads to output don't care.

Applied to your problem:

Resulting minimized expression for $f + g$:

x3' + x1' x2' + x1 x2 x5 + x2 x4 x5'