Introduction to the Algebra of Boole.

There are 256 possible logic circuits that can be constructed with 3 binary inputs and one binary output. Each circuit can be represented as a polynomial in the 3 inputs x, y, and z:
f(x,y,z) = a + bx + cy + dxy + ez + fxz + gyz +hxyz
By setting the 8 parameters {a,b,c,d,e,f,g,h} to the appropriate values, it is possible to exactly emulate any one of these 256 possible circuits.