Digital Logic 1/Boolean Logic

=Basic Ideas and Concepts=
 * What is a truth table and what can it do
 * Mapping a function on a truth table and determining all possible outputs
 * Applying principles of Boolean Algebra to minimize given function
 * Learn how to apply minterms and maxterms expansion to a truth table

=Truth Tables= A truth table is basically a representation of all the possible input combinations and the functional output of each of those combinations. It will tell you on a case-by-case basis, what will the functional output be in every input instance.

We need a way to represent the 3 basic logic operations in algebraic formulas. (AND, OR, NOT) Therefore we adopt the following standards for those representations: A AND B = $$A \cdot B = AB \! $$ A OR B = $$ A + B \! $$ NOT A (Inverted A) = $$ \overline{A} \!$$

For a simple example, a truth table of the AND gate is given below.

In general the number of rows in a truth table will be $$ 2^n,\!$$, where n is the number of variables. So in a 3 variable function where all the inputs are products, the following would be the truth table.

=Boolean Algebra= We introduce rules of Boolean Algebra to help us deal with simplifying more complex functions. The rules that should be learned are as follows.

=Activity=

Formulate a truth table for the given function below:

$$f(a, b, c)=\overline{a}bc + bc + \overline{ab}c \!$$