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Who knew how easy it would be to derive a Boolean expression from a truth table? By following a few simple steps, sum-of-products expressions are quickly converted to and from truth tables. In addition, the SOP expression is a heck of a performer.

Because many students have trouble when trying to simplify Boolean expressions, we're going to dedicate another episode to examples of simplification. We're also going to show how sometimes, there's more than one way to crack an egg.

In this episode, we take a break from proving identities of Boolean algebra and start applying them. Why? Well, so we can build our Boolean logic circuits with fewer gates. That means they'll be cheaper, smaller, and faster. That's why.

In this episode, we add one more tool to our Boolean algebra toolbox: DeMorgan's Theorem. We then use it, along with some of our other tools, to modify an expression down to its simplest form.

We are familiar with algebraic laws such as multiply zero by anything, and we get zero. In this episode, we see how a Boolean expression containing a constant, a duplicated signal, or a signal being combined with its inverse will simplify...always.

In this episode, we bring together our knowledge of logic operations, truth tables, and Boolean expressions to prove some basic properties of Boolean algebra.

Truth tables and circuit diagrams fall short in many ways including their abilities to evaluate and manipulate combinational logic. By using algebraic methods to represent logic expressions, we can apply properties and identities to improve performance.

The simplest combinational logic circuits are made by inverting the output of a fundamental logic gate. Despite this simplicity, these gates are vital. In fact, we can realize any truth table using a circuit made only from AND gates with inverted outputs.

Individual logic gates are not very practical. Their power comes when you combine them to create combinational logic. This episode takes a look at combinational logic by working through an example in order to generate its truth table.

In this episode, we introduce one of the most important tools in the description of logic operations: the truth table. Not only do truth tables allow us to describe a logic operation, they provide a means for us to prove logical equivalence.