Logic Gates/ Truth Tables Trouble

[Diearduk]

Hey guys I am having todo a resit paper for a maths module i failed and I've come up against a question on my paper where I am stomped and don't know if I am down the right road or not. Its truth tables from Boolean equations.

Question was:

K = ( X + Y) . (X . Y)

I Came up with:

K [U][B]X[/B][/U] Y | X Y K | K
1 0 0   1 1 1   1
1 1 1   0 0 0   0
1 0 1   1 0 0   0
0 1 0   0 1 0   0

Answer would be handy if i could get it and also where I've gone wrong and how todo it as there's a few more like this and worse. I've bolded and underlined for Inverted attributes as the forum code doesn't let me space out to do the _ sign midline.
Thanks

 

[chiro]

Hey Diearduk and welcome to the forums.

Your table is wrong: you need to use the same x and y values for each operation. I will create a new table and create an extra variable corresponding to the inverted X.

X Y Z = NOT X |  Z OR Y | X AND Y | (Z OR Y) AND (X AND Y)
0 0  1           1            0                  0
0 1  1           1            0                  0
1 0  0           1            0                  0
1 1  0           1            1                  1

We can use distributive laws to show that:

(NOT X + Y) . (X . Y) = (NOT X).X.Y + Y.X.Y = X.Y which is what we got above.

You should use these kinds of simplifications to give another check of whether you get something symbolic that matches up with your truth table.

 

[Diearduk]

Thanks Chiro, This forum and community looks great. Glad i could find it and thanks for your help :) Quick question tho was the Z meaning K? or was that the extra variable you made? i had a lecturer who really didnt educate anyone and just rambled on without explaining things :( meaning my whole class is pretty much as stomped as me.

 

[phinds]

Thanks Chiro, This forum and community looks great. Glad i could find it and thanks for your help :) Quick question tho was the Z meaning K? or was that the extra variable you made? i had a lecturer who really didnt educate anyone and just rambled on without explaining things :( meaning my whole class is pretty much as stomped as me.

Look at his table. He specifically says Z=not X. It's just to make the simplification look less confusing.

 

[rezeew]

I understand that truth tables and Boolean equations can be challenging. It looks like you have correctly created the truth table for the given Boolean equation. However, I would suggest double-checking the values in the last column (K) to ensure they are correct. Additionally, you may want to review the basic principles of Boolean algebra to ensure you fully understand the concepts and how to manipulate them to solve equations. There are also many online resources and tutorials available to help with understanding and solving truth tables and Boolean equations. Best of luck on your resit paper.