I am currently taking a Discrete Mathematics course, along with Intro to Hardware course. I am having issues wrapping my head around Boolean Theorems, simplifying functions given to smaller circuit design. One problem that I am working on at the moment is:
F
(a,b,c)= (A + C)(AB + AB`) + AC + C
I want to apologize for the formatting, but I did not see a shortcut in the toolbar above to format it correctly. I read through the theorems in the book, but I ended up finding my self more confused then I started with. I am looking for assistance in simplifying the function above, and also any help on tackling functions in the future.
I did construct a truth table to help determine how to simplify the function. From looking at the truth table, I did see that (A+C) & the function above have the same output. This conclusion seems as if (A+C) would be the simplified version of the original function, or at least be in the simplified version.
I know it is plain suicide taking both courses together, but somehow I have to overcome this hurdle. I appreciate any help provided.
Thank you,
~ KeiU
Here are some equalities that should get you to simplify your expression to $A+C$:
Adjacency
$AB+AB'=A$
$(A+B)(A+B')=A$
Absorption
$A+AB=A$
$A(A+B)=A$