I missed one question that asked for the simplified expression of a K-map. The function ended up being F(x,y)= x’ + y’, however because the question asked for the simplified version I used DeMorgan’s Law and simplified to F(x,y) = (xy)’ and was marked wrong. I am trying to understand why this was incorrect. Thoughts?
Hi, and welcome to the community!
You are correct, both options do evaluate to the same result. The reason one is incorrect and the other is correct is just a matter of convention.
Quoting from the bottom of the “Boolean Algebra” article in the prepawork:
You have seen, now, that you can express Boolean functions as truth tables or different Boolean expressions. In fact, there are an infinite number of Boolean expressions that are logically equivalent to one another. Two expressions that can be represented by the same truth table are considered logically equivalent.
To help eliminate potential confusion, people that use logic to design solutions specify a Boolean function using a unique standardized form. The two most common standards are sum-of-products form and product-of-sums form.
The sum-of-products form requires that the expression be a collection of
ANDed variables that are
ORed together. The expression
xy + yz' + xyzis in sum-of-products form. The expression
xy' + x(y + z')is not in sum-of-products form. You can apply the Distributive Law to the
xvariable to get
xy' + xy + xz'which is now in sum-of-products form.
The product-of-sums form consists of
ORed variables that are
ANDed together. This is more confusing and harder to use than the sum-of-products form. Most people use the sum-of-products form for that reason.
So, given this background,
(xy)’ is not in either of the two accepted formats (sum-of-products or product-of-sums).
x’ + y’, on the other hand, is a better answer because it is in the sum-of-products form.
Explained a different way, think about using DeMorgan’s law in the opposite direction: When simplifying, instead of using it to add the parentheses, use it to try to take away the parentheses.
Let me know if this explanation helps at all!
Thank you that helps!