Episodes
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Digital data has many benefits, but what happens if it's in error? Moreover, how can we tell if a bit has been flipped? Our discussion begins with parity.
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Having learned how to program bitwise operations, it is now time to flex our bit bashing muscles by investigating some creative ways to perform common programming functions.
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Missing episodes?
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Inverting or flipping the bits of an integer is the third and last method of "bit bashing" we will discuss. There are two ways to invert bits: either flip all of them at once or use a mask to identify which bits to flip and which to leave alone.
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The ability to set bits may not seem important at first, but many algorithms in computing depend on just that. Join us as we control bits and build integers from scratch using the bitwise-OR.
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Discussing how to use bitwise operations to manipulate the bits of an integer would be academic if we couldn't perform the operations in our code. The good news is that we can!
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Clearing bits within an integer is important if we want to isolate bits or set them to zero before we insert a new value. The bitwise-AND does this for us.
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All areas of computing, from data compression to web design, from networking to digital image storage, from system administration to high-performance computing, benefit from bit manipulation.
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A demultiplexer takes a single data stream and routes it to a selected output channel, a bit like one of those old A-B printer switches we used to physically select which printer we were sending data to. In this episode, we show how to design one.
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A multiplexer, sometimes referred to as a data selector, allows us to select which digital stream to route to an output. Designing this circuit is a lot easier than it sounds.
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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.
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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.
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This short episode shows how a complicated truth table can be clarified by using "don't cares" to represent input values.
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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.
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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.
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Let’s expand the capabilities of Karnaugh maps to combine more than just two rows of the truth table into a single product.
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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!
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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.
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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.
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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.
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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.
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