

In the truth table for a Boolean function, is there a reason why we should only select the rows that result in the outcome of 1?

Administrator

Since I don't have access to the Coursera course, I'm not quite sure what you are referring to without more info, so I'm inferring quite a bit here.
When implementing a logic function, a very common way of doing it is as an OR of all of the combinations of inputs that result in the function being TRUE (i.e., a 1). When doing this, we take each row of the truth table for that function that produces a 1 and use and AND gate to produce a logic HI for that particular set of inputs. We then combine the outputs of all of these AND gates with an OR gate.
Hope that helps.


Thank you WBahn
It helps and I know the process actually.
But, my real question is, why do we use only the outcomes where the function is TRUE, why did we neglect the outcomes that result is FALSE?
What is the reason?

Administrator

Because the cases where the function is FALSE is automatically taken care of by the OR gate.
If you have three cases where the function is TRUE, and each of those three cases if covered by an AND gate that produces a TRUE when the case it is looking for applies, and then you take the output of each of those AND gates and apply them to a 3input OR gate, the output will be TRUE whenever any of those those three cases applies, right?
But what will be the output when NONE of those three specific cases applies? Well, what is the output of an OR gate when none of it's inputs are TRUE? What output do we need our function to produce when none of the cases that should produce a TRUE applies?


Thank you.
I see the logic. Just as you said, other outcomes are automatically taken care of by the binary operator OR.
Indeed, output of an OR is FALSE when none of the inputs is TRUE.

