# Logic gate XOR and XNOR

1. Oct 10, 2008

### 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

2. Oct 10, 2008

### 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

3. Oct 10, 2008

### 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

4. Oct 12, 2008

### speck

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

5. Oct 12, 2008

### Phrak

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

Last edited: Oct 12, 2008
6. Oct 13, 2008

### 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 gotta 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

Last edited: Oct 13, 2008
7. Nov 15, 2008

### 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.

Last edited: Nov 15, 2008
8. Nov 15, 2008

### Enthalpy

(A xnor C) nor (B xor M)