How can I simplify this circuit using boolean algebra for XOR and XNOR gates?

[speck]

I want to simplfy M'(A'B'C+ABC')+M(AB'C'+A'BC) to as simple a circuit as possible.

I don't know the boolean algebra to simplfy the ABC terms. Help please, Speck

 

[rootX]

Tried K-maps?

From quick Venn inspection of (A'B'C+ABC') and (AB'C'+A'BC), I don't think you can simplify them further using AND, OR, NOT only

 

[speck]

K-map is how I initial got the Eq. , right, it won't simplify with AND, OR, NOT. I want to use XOR with XNOR gates. I would really like it to simplify to something like (AB Oplus C) using XOR, but it does not. Thks, Speck

 

[speck]

Does anyone think that the (A'B'C+ABC') part of the Eq. will reduce to (A Oplus B Oplus C)?

 

[Phrak]

By simple, do you mean the least number of packages? It's trivial with a single PLA, but you'd need a burner...

 

[rootX]

I tried to put it into XOR/XNOR but I really couldn't find any way.

P.S. (I learned this stuff few weeks ago, so all I know is that there should be checkboard pattern)

Now that I said that I realized that there is infact a pattern and it is easier to isolate it when you look at it. You got to approach it differently.
See K-Map When A = 0 and C = 1
A = 1 C = 0

I get something like

A!C!(B XOR M) + A!C (M XOR B)

So far, I look at K-Map and try to isolate 2 literal K-Maps that look like XOR and "and" it with conditions like A = 1 and C = 0 .. It works so far

 

[Enthalpy]

Another PLA-type cheater's answer: use a multiplexer. Input ABCM as the addresses, hardwire the 16 inputs to 1 or 0 to synthetise the desired logic function. The 4067 is such a 16-to-1 mux-demux and seems to be still relatively common (hey, I just feel younger!). One single package, no programming needed.

For a non-cheater answer, you'll have to wait a bit more. M and B have similar roles, as do A and C, so combining these pairs first could bring something.

 

[Enthalpy]

(A xnor C) nor (B xor M)
please check!

It's not "the simplest" form for the number of packages on a breadboard.

In a chip, I guess it's not the minimum number of Mos neither, as an xor or an xnor needs two inverters and 8 transistors, and a 16-to-1 mux also needs one inverter per input and this function consumes 16 N-channels and 16 P-channels.

Well, this form must be the simplest in the mind of some teacher at least.