SOLUTION: Simplify the following functions using a K-map F(X, Y) = m2 + m3 Can you explain me this homework question step-by-step? Thank you very much!

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Question 1191396: Simplify the following functions using a K-map

F(X, Y) = m2 + m3

Can you explain me this homework question step-by-step? Thank you very much!
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Here are the standard minterms for 2 variables only.
Minterms
XYTermDesignation
00X'Y'm0
01X'Ym1
10XY'm2
11XYm3


This is the blank K-map for the two variables X and Y.

Along the top we have 0 and 1 corresponding to either X' or X respectively.
Along the left side we have 0 and 1 corresponding to either Y' or Y respectively.
These rules apply to minterms only.

Inside the table itself, we'll enter the m0 through m3 as shown below.

Here's some informal notation to help keep track.
m0 = 00 = X'Y'
m1 = 01 = X'Y
m2 = 10 = XY'
m3 = 11 = XY
Or you could use the minterm table mentioned at the top of the page.

Next, we replace m2 and m3 with 1's since they are part of the F(X,Y) function.
The other minterms get replaced with 0s


Now comes the grouping.
Use these K-Map grouping rules
http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karrules.html
and you can review on this page if needed
http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karnaugh.html#introduction
There are a lot of rules to keep in mind, but once you get the hang of it, it's not too bad.

Luckily in this problem, we really don't have to bother with those rules because we have a fairly trivial grouping along the right column.
So we end up with XY'+XY = X(Y'+Y) = X*1 = X

Answer: X