Hello Everybody, this is my first post.

I have a "strange" question on Boole's truth tables, So i better start with an example.

Lets say that i have three Digital Inputs X, Y and Z and 1 digital Output Q

Also i have a Boole's expression that determines the Output : Q = X+Y+Z (Where * => logical AND and + => Logical OR)

The Truth table representing this expression is:

The problem is to "Brake" this Truth table into 2 other truth tables with 2 inputs each. We are able to use "virtual" inputs representing with lower case letters a, b, c, ...

X Y Z Q 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1

Well in a simple example like that the solution is obvious:

The first truth table would be :

And the second truth table would be:

Y Z a 0 0 0 0 1 1 1 0 1 1 1 1

Now my question is, if i have a complex expression which produces a complex truth table, lets say:

a X Q 0 0 0 0 1 1 1 0 1 1 1 1

Is it possible to "Brake" this truth table into 2 other truth tables with 2 inputs each?

X Y Z Q 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0

And if Yes, How it can be generalized to "Break" multiple input truth tables to others with 2 inputs each?

Thanks in advance.