We went over section 8.1: Boolean
Algebras, and saw how it is a generalization of both
propositional logic and set theory.
The basic five properties (or "axioms") are exactly the
same as those we've encountered in logic and set theory.
From these basic properties we proved a couple of
additional properties, such as
idempotence, and the universal bound property.
We also established that complements are unique.
Propositional logic can be thought of as the world's
simplest Boolean algebra, where the two elements are
\(\{0,1\}\), with the binary operations of \(\land\), \(\lor\), and
the unary operation of negation (\('\)).
We'll be working with variables that take the value of 0
and 1, Boolean variables, and try to reduce Boolean expressions
to their simplest forms.
Today:
We continue with section 8.2: Logic
Networks, with the objective to implement truth functions
in hardware via Boolean expressions, which we simplify using
strategies which will be further studied in section 8.3.