Question 1191424: Simplify the following functions using a K-map
F(X, Y) = X’ + XY’
Can you explain this other homework question step-by-step please? Thanks again!
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to simplify F(X, Y) = X' + XY' using a K-map:
1. **Set up the K-map:** Since there are two variables (X and Y), the K-map will be a 2x2 grid:
```
Y
0 1
X 0 X'Y' X'Y
1 XY' XY
```
2. **Fill in the K-map based on the function:**
* **X'**: This term is true when X=0, regardless of the value of Y. So, we fill in both cells in the top row (X=0) with 1s.
* **XY'**: This term is true when X=1 and Y=0. So, we fill in the cell where X=1 and Y=0 with a 1.
```
Y
0 1
X 0 1 1
1 1 0
```
3. **Group the 1s:** We want to make the largest possible groups of 1s, where the groups are powers of 2 (1, 2, 4).
* **Group 1:** The two 1s in the top row form a group of 2. This group represents X' (because X=0 for both cells).
* **Group 2:** The 1 at X=1 and Y=0 is already as large a group as it can be. This represents XY'.
4. **Write the simplified expression:**
The simplified expression is simply the sum of the groups:
F(X, Y) = X' + XY'
In this particular case, the function is *already simplified*. The K-map just confirms that there are no further simplifications possible.
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