
Truth Table
So the actual application for this is logic gates, kmaps, and circuits, but the logic is basically just math.
Say I have the following formula...
A + BAC + D
I think you guys would probably prefer to see it like this
A => (B & ¬A & C) => D
Would this result in
A B C D  F
0 0 0 0  0
0 0 0 1  1
0 0 1 0  0
0 0 1 1  1
0 1 0 0  0
0 1 0 1  1
0 1 1 0  1
0 1 1 1  1
1 0 0 0  1
1 0 0 1  1
1 0 1 0  1
1 0 1 1  1
1 1 0 0  1
1 1 0 1  1
1 1 1 0  1
1 1 1 1  1
If i'm just checking for A, i will mark EVERYTHING that has a 1 in the A column as a 1, right?

The setup looks correct. Since there are 4 variable sthere will be $\displaystyle 4^4$ rows which you have is correct. Now we will nee dto fill in all of the possible combinations within the columns. My column a has 8 true cells followed by 8 false cells. My column b has 4 true cells followed by 4 false cells, and this keeps on rottaing until all cells are filled. My column C has two true cells followed by 2 false cells and this keeps on rottaing until all cells are filled. Last, column D has a true cell followed by a false cell and this keeps on rotating. It looks correct.