Convert from a closed form to the truth table using Boolean functions?

Questions
1

Hello!

I would like to understand how to work with boolean functions in a better way. Can you show me how to convert from a closed form to the truth table, ANF or DNF? For example, say I have a polynomial on four variables,

f(w,x,y,z) = wx + yz

This should be in ANF like this:

[Xor[x1x2,x3x4]
so I feel like I should be able to get Mathematica to spit out a truth table, but this>

Boole[BooleanTable[Xor[x1*x2, x3*x4]]]

does not work at all.

How can I get the truth table from that? Doing it out by hand gets old real fast:)

Thanks!
Mary

2

What do you mean by multiplication? In Mathematica True and False are NOT treated as 1 and 0. So one can not create an AND function by multiplying. Use the proper functions: And, Or, Xor, Nand, Nor, Xnor et cetera. Furthermore BooleanTable needs a second argument with the variables…

3

Something like this?

In[1]:= Boole@BooleanTable[
  	Xor[
   		And[x1, x2],
   		And[x3, x4]
   	],
  	{x1, x2, x3, x4}
  ]

Out[1]= {0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0}