K-Map Homework: Solving (x+y)(x+y')

[Heat]

Homework Statement

I understand the basic of kmaps like
xy+xy' =
y y'
x 1 1
x' 0 0

would be x.

but when we have (x+y)(x+y'), how would that be setup?

 

[LCKurtz]

Homework Statement

I understand the basic of kmaps like
xy+xy' =
y y'
x 1 1
x' 0 0

would be x.

but when we have (x+y)(x+y'), how would that be setup?

The easiest way is change the product of sums to a sum of products by "multiplying it out" using the properties of and, or, and complement and simplifying. Alternatively you can evaluate the expression for the four possibilities (x,y) = (0,0) or (0,1) or (1,0) or (1,1) in fill in the K- table with the results.

 

[Mene]

Hello! It seems like you are trying to solve a K-Map for the expression (x+y)(x+y'). In order to do this, we need to first expand the expression using the distributive property. This gives us (x^2 + xy' + xy + yy').

Next, we can simplify this by combining like terms. In this case, we can see that the terms xy and xy' are the same, so they can be combined to give us (x^2 + 2xy').

Now, we can use the K-Map to represent this expression. Since there are two variables, x and y, we will need a 2x2 K-Map. The rows and columns of the K-Map will represent the four possible combinations of x and y, with the top row representing x=0 and the bottom row representing x=1, and the left column representing y=0 and the right column representing y=1.

In the K-Map, we will fill in the values of (x^2 + 2xy') for each combination of x and y. This will give us the following K-Map:

y y'
x x^2 2xy'
x' 0 0

From this, we can see that the simplified expression for (x+y)(x+y') is x^2 + 2xy'. I hope this helps you understand how to set up a K-Map for this type of expression. Keep up the good work with your K-Map homework!