This blog entry won't serve as an introduction to Boolean Algebra or logic gates, but rather just to illustrate an HTML5 widget I wrote that lets you manipulate NAND gates. In fact, before you begin, you should understand what these tables mean:
NOR = f(a,b) NAND = f(a,b) a b f a b f 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0
If that makes no sense, start with this Wikipedia article on logic gates.
In the early 20th century, the maths world went wild trying to expand on George Boole's work on logic. Ernst Schröder, Edward Huntington, and Alfred Whitehead each developed conflicting notation systems and postulate sets, each with published works that were pretty arcane. For instance: