It’s time to do a series on logic including things such as programmable logic, state machines, and the lesser known demons such as switching hazards. It is best to start at the beginning — but even experts will enjoy this refresher and might even learn a trick or two. I’ll start with logic symbols, alternate symbols, small Boolean truth tables and some oddball things that we can do with basic logic. The narrative version is found in the video, with a full reference laid out in the rest of this post.
The most simple piece of logic is inversion; making a high change to low or a low change to high. Shown are a couple of ways to write an inversion including the ubiquitous “bubble” that we can apply almost anywhere to imply an inversion or a “True Low”. If it was a one it is now a zero, where it was a low it is now a high, and where it was true it is now untrue.
Moving on to the AND gate we see a simple truth table, also known as a Boolean Table, where it describes the function of “A AND B”. This is also our first opportunity to see the application of an alternate symbol. In this case a “low OR a low yields a low”
Most if not all of the standard logic blocks come in an inverted form also such as the NAND gate shown here. The ability to invert logic functions is so useful in real life that I probably used at least three times the number of NAND gates as regular AND gates when doing medium or larger system design. The useful inversion can occur as spares or in line with the logic.