Boolean algebra help

[RESmonkey]

I got 2 out of 3 correct.

Why is the last one true? I just can't simplify my expression into that.

http://img362.imageshack.us/img362/342/whyyyycj7.jpg

 

[Shadow Conception]

Wow, I think I got lucky in my Digi Electronics course... never had any questions asking for incompletely simplified expressions.

 

[JohnCU]

its sad when you lose what you don't use

i wrote it out but can't figure it out either

 

[RESmonkey]

 

[TehJustinator]

So,

the first XZ and X'YZ' can be seen from the first and third and respectively. The second and is X'Y'Z. Wouldn't the X' be implied because if it were X, then XZ would be true and so we'd receive a true from the or?

 

[RESmonkey]

^ how would the x' be implied:

XZ + X'Y'Z + X'YZ' =?= XZ + Y'Z + X'YZ'

X'Y'Z =?= Y'Z

X' <---wtf

 

[JohnCU]

email your professor that's what i always did

 

[TehJustinator]

X'Y'Z =/= Y'Z

XZ + X'Y'Z == XZ + Y'Z

Look at Y'Z. We're asserting both NOT Y and Z. If we're asserting NOT Y and Z then we don't care about X. If X is true, then XZ will return true and thus F will be true. If it's false, then Y'Z will return true. I don't remember any specific rules to simplify it in such a way, but looking at the diagram should suffice as a basis.

 

[RESmonkey]

Thanks guys, I posted it on the help section of the class's forum.

I feel like I'm in the wrong major

 

[RESmonkey]

Originally posted by: TehJustinator
X'Y'Z =/= Y'Z

XZ + X'Y'Z == XZ + Y'Z

Look at Y'Z. We're asserting both NOT Y and Z. If we're asserting NOT Y and Z then we don't care about X. If X is true, then XZ will return true and thus F will be true. If it's false, then Y'Z will return true. I don't remember any specific rules to simplify it in such a way, but looking at the diagram should suffice as a basis.

I don't understand. You don't know if Z is true or not.

 

[TehJustinator]

Originally posted by: RESmonkey

Originally posted by: TehJustinator
X'Y'Z =/= Y'Z

XZ + X'Y'Z == XZ + Y'Z

Look at Y'Z. We're asserting both NOT Y and Z. If we're asserting NOT Y and Z then we don't care about X. If X is true, then XZ will return true and thus F will be true. If it's false, then Y'Z will return true. I don't remember any specific rules to simplify it in such a way, but looking at the diagram should suffice as a basis.

I don't understand. You don't know if Z is true or not.

Yes, we have no clue if Z is true or not...If Z is true though then the third gate will be false. So we look at the first two. The first depends on X and Z being true, while the second on X', Y' and Z. If X is true then the first gate will be true and that will be sufficient for a true from the or gate. If Y' is true and X is true and Z is true then the first gate will return true. This is again sufficient for our or to return true. If X' is true and Y' and Z are true again, then only the second returns true. Again sufficient for a true from the gate. The X' can be removed because we know that regardless if X is true or not, if we have a Y' and a Z then we will receive a true from the or (If X is true we'll get what we need from the first gate).

X'Y'Z cannot and will not be equivalent to Y'Z on its own ever, you're right about that. But by ORing XZ in there, we can remove the X' from X'Y'Z because regardless of the value of X in the Y'Z, we will get the correct value from the OR gate if a Y' and Z are true.

 

[CrazyHelloDeli]

The answer: GOD

 

[Minjin]

It should be one of your identities. Factor and apply your identity and you'll see how it can reduce down to that form.

 

[esun]

Easy. Start with the expression from (a):

X'Y'Z + X'YZ' + XY'Z + XYZ

Note this is the same as:

X'Y'Z + X'YZ' + XY'Z + XYZ + XY'Z

Note that I've just copied one of the terms again (the 3rd term). That doesn't change the truth value of the expression (consider, if A + B is true, then A + B + B is true, and vice versa).

Now, I can factor XZ from the 3rd and 4th terms and I can factor Y'Z from the 1st and 5th terms:

XZ(Y' + Y) + Y'Z(X' + X) + X'YZ'

Note that A + A' = true always, so we have:

XZ + Y'Z + X'YZ'

Which is the expression in (c) exactly.

 

[GML3G0]

Well, you could just express each of those expressions in their standard sum of products form.

Multiply each product in the expression that's missing a term by (missing term + inverse of missing term).

XZ + X'Y'Z + X'YZ' = XYZ + XY'Z + X'Y'Z + X'YZ'

Choice 3, XZ + Y'Z + X'YZ' becomes:

XYZ + XY'Z + X'Y'Z + XY'Z +X'YZ' = XYZ + XY'Z + X'Y'Z + X'YZ'