Question 1191165: Simplify the following functions using a K-map
a. F(X, Y) = m2 + m3
b. F(X, Y) = X + X’Y
c. F(X, Y) = X’ + XY’
d. F(X, Y, Z) = m0 + m2 + m5 + m7
e. F(X, Y,Z) = X’Y’Z’ + X’YZ + XY’Z + XYZ
Can you please explain to me this homework question step-by-step? Thank you!
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's the simplification of the given functions using K-maps:
**a. F(X, Y) = m2 + m3**
```
Y
X 0 1
0 0 1 (m2)
1 0 1 (m3)
```
Grouping m2 and m3, we get:
F(X, Y) = Y
**b. F(X, Y) = X + X’Y**
```
Y
X 0 1
0 1 1
1 1 1
```
Grouping all the 1s, we get:
F(X, Y) = 1
**c. F(X, Y) = X’ + XY’**
```
Y
X 0 1
0 1 1
1 1 0
```
Grouping the top row and the single 1 at X=1, Y=0 we get:
F(X, Y) = X' + Y'
**d. F(X, Y, Z) = m0 + m2 + m5 + m7**
```
YZ
X 00 01 11 10
0 1 0 1 1
1 0 1 1 0
```
Grouping m0 and m2, and m5 and m7:
F(X, Y, Z) = X’Y’ + YZ
**e. F(X, Y,Z) = X’Y’Z’ + X’YZ + XY’Z + XYZ**
```
YZ
X 00 01 11 10
0 1 1 0 1
1 1 1 1 1
```
Grouping the top row, and the bottom row, we get:
F(X, Y, Z) = Y' + Z
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