How Can I Simplify This Boolean Expression Using XOR and XNOR Functions?

[TheTopGun]

Homework Statement

Hey there, I'm having trouble simplifying a boolean expression using XOR and XNOR functions.
The final goal is to draw a logic circuit for the expression using NAND and XOR gates only.

Homework Equations

Assuming
W' = Not WW' X' Y' Z' + W' X' Y Z + W' X Y' Z + W' X Y Z' + W X Y' Z' + W X' Y' Z

The Attempt at a Solution

W' X' (Y⊕Z)' + W' X (Y⊕Z) + ...

So far if I'm working correctly (?) I can simplify the first four expressions, It's just the last two that get me as they have no like terms ?

Once I understand this I should have no troubles drawing the logic circuit.

Thankyou for any responses

 

[jedishrfu]

you could try drawing a truth table for the terms and see if you spot a pattern that matches XOR or NAND

like X xor Y'

 

[TheTopGun]

Hmm okay thanks,

I've come up with this

W' X' (Y⊕Z)' + W' X (Y⊕Z) + W Y' (X⊕Z)

Is this on the right track..before I simplify further.

 

[NascentOxygen]

W x y' z' + w x' y' z = w y'❲ ... ❳

wow, PF has such a nanny editor that it converted my upper case to lower!

 

[jedishrfu]

Hmm okay thanks,

I've come up with this

W' X' (Y⊕Z)' + W' X (Y⊕Z) + W Y' (X⊕Z)

Is this on the right track..before I simplify further.

That seems right. Once complete you could do a truth table on it and see if it agrees with original.

 

[NascentOxygen]

Hmm okay thanks,

I've come up with this

W' X' (Y⊕Z)' + W' X (Y⊕Z) + W Y' (X⊕Z)

Is this on the right track..before I simplify further.

You can see how to simplify this further? If not, I suggest that you construct a 4 variable Truth Table. Also construct the Truth Table for your simplified expression, and with any luck there may be some correspondence.

I haven't tried it.

 

[TheTopGun]

For future reference (im not sure why anyone would care lol, but anyway), the equation can be simplified down to:

W' (X⊕Y⊕Z)' + Y' (W⊕X⊕Z)' ...where (A⊕B⊕C)' represents a XNOR gate.

This was obtained using karnough maps but I am sure there are easier ways...