Geek Author

What does it take to switch on a device? In some cases, like getting a soda from a vending machine, a number of conditions must be just right. That's where binary decoders come in.

Sometimes, it's nice to take a look at old tech to learn a new tool. The 7-segment display has been in our lives for years - mostly in alarm clocks. Join us as we use a Karnaugh map to design a driver for one.

This short episode shows how a complicated truth table can be clarified by using "don't cares" to represent input values.

Like a wild card in a game of poker, an unspecified truth table entry called a "don't care" can make our sum-of-products expressions so much nicer.

Many digital designs begin with a truth table. In this episode, we do just that, and then create the simplified sum-of-products expression by way of the Karnaugh map.

Let's expand the capabilities of Karnaugh maps to combine more than just two rows of the truth table into a single product.

To make the move to a four-variable Karnaugh map, we are going to double the number of columns found in the three-variable map. And what happens when we halve the three-variable map? We get a two-variable Karnaugh map!

Here we introduce a graphical tool that when used correctly will produce a most simplified sum-of-products expression, all without meddling in any simplification of Boolean expressions.

Now that we've studied the sum-of-products form of Boolean expressions, it's time to take a look at the product-of-sums. This form uses logical OR's to generate zeros which are passed to the output through an AND gate.

The NAND gate outputs a logic zero only when all its inputs equal logic one. Let's explore how this universal gate can be used to implement any Boolean expression.