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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.

Logic gates are the fundamental building blocks of digital circuits. In this episode, we take a look at the four most basic gates: AND, OR, exclusive-OR, and the inverter, and show how an XOR gate can be used to compare two digital values.

By examining Run Length Limited (RLL) coding, we discover a way to compress the ones and zeros of our binary data by using differential coding. We also chat a bit about magnetic storage media.

In this episode, we continue our discussion of line codes by examining five schemes used with polar and bipolar signaling: NRZ-L, NRZ-I, RZ-AMI, Manchester, and differential Manchester. We also discuss differential coding and its benefits.

When sending digital data from one device to another, both devices must agree on how to represent ones and zeros. This episode presents how signal levels affect the delivery of data and how line codes are used to represent the ones and the zeros.

ASCII was developed when every computer was an island and over 35 years before the first emoji appeared. In this episode, we will take a look at how Unicode and UTF-8 expanded ASCII for ubiquitous use while maintaining backwards compatibility.

In 1963, the American Standards Association released a standard defining an 8-bit method to represent letters, punctuation, and control characters. This episode examines ASCII so that we can begin to see how computers represent language.

Regardless of the numeric base, scientific notation breaks numbers into three parts: sign, mantissa, and exponent. In this episode, we discuss how the computer stores those three parts to memory, and why IEEE 754 puts them together the way it does.

Up to this point, we've limited our discussion to binary integers. In this episode, we are moving the curtain to reveal the powers of two to the right of the binary point in order to begin representing fractions.

It turns out that twos complement is just one of many ways to use binary to represent negative numbers. In this episode, we examine the use of offset or biased notation to represent signed integers.

In this episode, we continue our discussion of twos complement binary representation by covering overflow and how shifting left and right can be used to perform multiplication and division by powers of two.

In this episode, we switch from base ten to binary as we introduce twos complement representation and show how computers store and manipulate signed integers.