Circuit to Karnaugh map

Question

A logical circuit was given, I had to create a boolean expression from it; which I did correctly (I guess). I calculated the output of each gate separately, considering the variables.

From the given circuit I got this expression:

('xy + x) + ((x + y) + z) * 'u

I than would need to put this in a Karnaugh's map to simplify the expression (and later on the circuit). But this is the step I got stuck on.

How to put that expression in Karnaugh's map? Even when I perform algebra on the current expression I get terms which aren't present in the map, or single terms like only 'x', but 'only x' ain't present in the map.

I have already converted expressions to Karnaugh map with no problems, but I guess I have difficulty now because it's with 4 variables, and a tough expression.

Answer 1

HINT

To put a term like $x$ in the map, simply put a $1$ in all the cells where $x$ is true.

So, in your kmap, that would be the top four cells as well as the bottom four cells.

Also, to find the terms to put into the map, it helps to first put it into DNF:

$$x'y+x+((x+y)+z)u'=x'y+x+xu'+yu'+zu'$$

Answer 2

Sorry, I couldn't send any photo.
Your function is false when $xyzu = {0000, 0001,0011}$.
First and second columns are when $x$ = true (1), another columns are false (0).
Second and third columns are when $y$ = true (1), another columns are false (0).
First and second lines are when $z$ = true (1), another lines are false (0).
Second and third lines are when $u$ = true (1), another lines are false (0).

$$1|1|1|1$$ $$1|1|1|0$$ $$1|1|1|0$$ $$1|1|1|0$$

As a result, $$f = x \lor y \lor \overline uz$$