Question

Expand the following Boolean functions into their canonical form:
i. f(X,Y,Z)=XY+YZ+ X Z+ X Y
ii. f(X,Y,Z)=XY+ X Y + X YZ

Answer 1

Answer on Question # 42970, Math, Discrete Mathematics

Task:

Expand the following Boolean functions into their canonical form:

i. $f(X,Y,Z) = XY + YZ + X'Z + X'Y$

ii. $f(X,Y,Z) = XY + X'Y + X'YZ$

Solution:

i. $f(X,Y,Z) = XY + YZ + X'Z + X'Y$

A table about the minterm:

Write the truth table:

To expand the following Boolean function into its canonical form we have to sum all the minterms (where the $f$ is equal to 1):

So, $f(X,Y,Z) = X'Y'Z + X'YZ' + X'YZ + XYZ' + XYZ$

ii. $f(X,Y,Z) = XY + X'Y + X'YZ$

Analogically:

So, $f(X,Y,Z) = X'YZ' + X'YZ + XYZ' + XYZ$

Answer:

i. $f(X,Y,Z) = X'Y'Z + X'YZ' + X'YZ + XYZ' + XYZ$

ii. $f(X,Y,Z) = X'YZ' + X'YZ + XYZ' + XYZ$