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.