WEBVTT - TechStuff Tidbits: Logic Gates and Headache Medication 0:00:04.440 --> 0:00:12.360 Welcome to Tech Stuff, a production from iHeartRadio. Hey thereon 0:00:12.480 --> 0:00:15.480 Welcome to Tech Stuff. I'm your host, Jonathan Strickland. I'm 0:00:15.480 --> 0:00:18.360 an executive producer with iHeartRadio. And how the tech are you? 0:00:19.280 --> 0:00:25.000 So I threatened? Sorry, I mean I mentioned last week 0:00:25.280 --> 0:00:28.400 that I planned to do an episode about logic gates, 0:00:28.720 --> 0:00:31.240 which light at the heart of computer processing. So today 0:00:31.280 --> 0:00:33.720 we're going to do a quick overview of logic gates 0:00:33.800 --> 0:00:36.120 and what they do. And originally I was going to 0:00:36.240 --> 0:00:39.000 run reruns this week because I'm actually on vacation as 0:00:39.040 --> 0:00:42.479 you listen to this, but I had a little extra 0:00:42.880 --> 0:00:45.800 pizazz in my step that I'll talk about in a second. 0:00:46.200 --> 0:00:48.760 But yeah, let's talk about logic gates and what they do. 0:00:48.800 --> 0:00:51.200 And first up, you should know that logic gates are 0:00:51.240 --> 0:00:55.560 based off of Boolean algebra. This branch of math was 0:00:55.560 --> 0:00:59.560 invented by the guy that it was named after, George Algebra. 0:01:00.520 --> 0:01:03.600 Just kidding. His name was George Bull. Bull was born 0:01:03.680 --> 0:01:07.440 in England in eighteen fifteen, as so many were. He 0:01:07.480 --> 0:01:10.000 died forty nine years later in Ireland. And I can 0:01:10.120 --> 0:01:13.920 understand why. I guess this is where I should mention. 0:01:13.959 --> 0:01:17.399 I'm writing this episode while under the influence of advil 0:01:17.520 --> 0:01:20.280 PM because I grabbed the wrong tablets while trying to 0:01:20.280 --> 0:01:23.520 treat a headache. So that's going to be a factor 0:01:23.959 --> 0:01:26.959 for the rest of this episode, just like you know. Anyway, 0:01:27.400 --> 0:01:31.400 George Bull helped establish symbolic logic, which, by the way, 0:01:31.680 --> 0:01:35.840 I loved that subject in college. It was a math 0:01:35.920 --> 0:01:40.000 course that I excelled at. In fact, I would only 0:01:40.080 --> 0:01:43.800 show up to class on Thursdays and Fridays. We met 0:01:43.800 --> 0:01:46.600 every day of the week, but there was no attendance policy. 0:01:46.959 --> 0:01:49.120 So Thursday I would show up to find out which 0:01:49.200 --> 0:01:52.680 chapters that the professor had gone over, and then Friday 0:01:52.680 --> 0:01:55.720 I would show up because there was a quiz for 0:01:55.840 --> 0:02:01.240 that week's lessons. And symbolic logic made so much sense 0:02:01.280 --> 0:02:03.880 to me that I could just show up on Thursday 0:02:03.920 --> 0:02:06.360 to see which chapters that needed to read, show up 0:02:06.360 --> 0:02:10.120 Friday and do the work. And I aced that class. 0:02:10.120 --> 0:02:11.760 Now this is not to say that I'm a genius. 0:02:11.800 --> 0:02:15.040 I am not. Just for some reason or another, symbolic 0:02:15.120 --> 0:02:17.640 logic clicked with me in a way that a lot 0:02:17.680 --> 0:02:21.120 of subjects never did. Anyway, symbolic logic would become a 0:02:21.160 --> 0:02:25.400 fundamental foundation for digital circuits. Years later, my guess is 0:02:25.480 --> 0:02:27.840 he didn't know that was going to happen because computers 0:02:27.880 --> 0:02:31.800 weren't a thing yet. So what had happened was Bull 0:02:31.880 --> 0:02:35.280 mostly learned mathematics all on his own. He received some 0:02:35.400 --> 0:02:39.119 tutoring from his father, who was a tradesman, and he 0:02:39.320 --> 0:02:43.320 did go to a couple of schools, but no like 0:02:43.960 --> 0:02:47.920 secondary formal education. Mainly he was self taught, and he 0:02:47.960 --> 0:02:52.520 actually began teaching around various schools in his region when 0:02:52.560 --> 0:02:55.840 he was just sixteen years old, not only because he 0:02:55.919 --> 0:02:59.160 was brilliant, but also because it was necessary. His father's 0:02:59.200 --> 0:03:02.040 business had slowed down and his family needed the income. 0:03:02.400 --> 0:03:04.680 So the gig economy has been around for a while, 0:03:04.680 --> 0:03:07.440 I guess is what I'm saying. In the eighteen forties, 0:03:08.040 --> 0:03:12.040 Bull submitted papers to the Cambridge Mathematical Journal on subjects 0:03:12.160 --> 0:03:16.560 ranging from differential equations to calculus, you know, light reading. 0:03:17.000 --> 0:03:20.000 In eighteen forty seven, he published a work titled the 0:03:20.040 --> 0:03:25.240 Mathematical Analysis of Logic Being an Essay toward a Calculus 0:03:25.280 --> 0:03:29.760 of Deductive reasoning. This landed him a university teaching gig, 0:03:29.800 --> 0:03:32.280 even though he had never earned a college degree of 0:03:32.280 --> 0:03:36.160 his own. In eighteen forty five, he published a further 0:03:36.240 --> 0:03:39.800 treatment of his ideas titled an Investigation into the Laws 0:03:39.800 --> 0:03:43.760 of Thought on which are founded the mathematical theories of 0:03:43.840 --> 0:03:48.480 logic and probabilities Real Page Turner. In eighteen forty six 0:03:48.800 --> 0:03:54.120 he married Mary Everest, the daughter of Mount Everest. Okay, wait, no, sorry, no, 0:03:54.320 --> 0:03:57.880 she was the daughter of George Everest. It's just that 0:03:57.960 --> 0:04:02.120 Mount Everest is named after George Everest. That's actually true. 0:04:02.800 --> 0:04:06.120 I got a little confused there. Sorry, I'm blaming the ADVILPM. 0:04:06.160 --> 0:04:11.320 At this point, Boole used mathematical symbols to represent logical 0:04:11.480 --> 0:04:15.520 arguments and showed that by encoding an argument as a 0:04:15.640 --> 0:04:18.800 series of equations, one could check to see if the 0:04:18.920 --> 0:04:22.760 argument was sound or not, if it were true, or 0:04:22.800 --> 0:04:26.880 if it were false. So, for example, maybe you were 0:04:27.120 --> 0:04:31.560 saying something like all cats are mammals, Old Greg is 0:04:31.600 --> 0:04:34.880 a cat, therefore old Greg is a mammal. Well, you 0:04:34.880 --> 0:04:38.080 could actually represent those statements as equations, and then you 0:04:38.120 --> 0:04:42.880 could solve to show that the conclusion is contained within 0:04:42.920 --> 0:04:47.160 the premises. So if the premisses contained the conclusion and 0:04:47.320 --> 0:04:49.960 everything lines up, you would say it's logically sound. It 0:04:50.120 --> 0:04:53.800 is a true argument. However, if you said all cats 0:04:53.839 --> 0:04:57.320 are mammals. Old Greg likes to sip Bailey's out of 0:04:57.360 --> 0:05:00.240 a shoe. Therefore, Old Greg is a mammal. Well, that 0:05:00.279 --> 0:05:03.880 wouldn't fly because you haven't established that Old Greg is 0:05:03.880 --> 0:05:06.440 a cat or any other kind of mammal for that matter. 0:05:06.680 --> 0:05:10.000 He's Old Greg. So what does this have to do 0:05:10.040 --> 0:05:12.839 with computers. Well, Old Greg will have nothing to do 0:05:12.920 --> 0:05:14.800 with computers, probably because he lives at the bottom of 0:05:14.800 --> 0:05:17.440 a lake and his computer with short circuit immediately. But 0:05:17.600 --> 0:05:22.920 boolean logic would underpin the concept of logic gates, which 0:05:22.920 --> 0:05:26.320 in turn would allow a computer to process information in 0:05:26.360 --> 0:05:29.440 a meaningful way. And this brings us to the concept 0:05:29.640 --> 0:05:34.320 of actual logic gates. PCMag dot com defines logic gates 0:05:34.360 --> 0:05:39.680 as quote a collection of transistors and resistors that implement 0:05:39.839 --> 0:05:44.080 boolean logic operations in a digital circuit. Logic gates have 0:05:44.400 --> 0:05:48.559 one or two zero or one inputs, but only one 0:05:49.160 --> 0:05:53.080 zero or one output, as in the following examples, which 0:05:53.279 --> 0:05:57.000 they then list to continue the quote. Transistors make up gates, 0:05:57.440 --> 0:06:02.520 Gates makeup circuits, and circuits may up electronic systems. End quote. 0:06:02.880 --> 0:06:09.160 So a typical logic gate usually accepts two inputs and 0:06:09.200 --> 0:06:13.520 produces a single output, and that output is based both 0:06:13.600 --> 0:06:15.760 upon the nature of the inputs and the nature of 0:06:15.760 --> 0:06:18.680 the gate itself. I say typically, because of course there 0:06:18.680 --> 0:06:22.680 are exceptions, but for the purposes of simplicity, we're mainly 0:06:22.720 --> 0:06:26.880 focusing on the typical example of two inputs enter, one 0:06:26.920 --> 0:06:31.440 output leaves. So yeah, I am going thunderdome with these rules. 0:06:32.240 --> 0:06:35.000 The output that a logic gate produces, like I said, 0:06:35.080 --> 0:06:38.000 depends both upon the value of the inputs and the 0:06:38.000 --> 0:06:40.520 type of logic gait that we're talking about. So you 0:06:40.520 --> 0:06:43.560 can think of logic gates being kind of like a 0:06:43.600 --> 0:06:48.120 physical gate that leads into, say a courtyard, and this 0:06:48.360 --> 0:06:51.760 particular gate has a bouncer standing outside of it. The 0:06:51.800 --> 0:06:54.920 bouncer enforces the rules. So you come up to the gate, 0:06:55.080 --> 0:06:58.240 and if you meet certain criteria, the bouncer lets you through, 0:06:58.440 --> 0:07:00.920 and if you do not meet the criteria, the bouncer 0:07:01.000 --> 0:07:04.880 turns you away. This analogy isn't perfect, because really the 0:07:04.960 --> 0:07:08.320 logic gates allow a value to pass through no matter 0:07:08.360 --> 0:07:11.160 what it's just what value is that going to be? 0:07:11.280 --> 0:07:13.640 Will it be a zero or will it be a one. 0:07:13.920 --> 0:07:17.040 So the bouncers in circuits are electronic components, and the 0:07:17.120 --> 0:07:19.840 rules depend upon the type of gait. And we are 0:07:19.960 --> 0:07:23.160 talking physical structures here in a circuit. We're actually talking 0:07:23.160 --> 0:07:27.480 about transistors and resistors. So the way the gates work 0:07:28.680 --> 0:07:33.640 is dependent upon voltage. So each input can have one 0:07:33.720 --> 0:07:37.840 of two values. Either zero volts is applied to the input, 0:07:38.000 --> 0:07:42.680 which would then represent an input of zero, or five 0:07:42.800 --> 0:07:46.840 positive volts are inputed into that input and then that 0:07:46.880 --> 0:07:51.040 represents a one. The output produces a value of either 0:07:51.160 --> 0:07:54.480 zero volts, so a zero in logic, or five volts 0:07:54.560 --> 0:07:57.680 again meaning a one in logic. Now, if we just 0:07:57.840 --> 0:08:03.520 talking two inputs, you can have four possible combinations, right, 0:08:04.000 --> 0:08:06.640 So each input can have one of two states, either 0:08:06.680 --> 0:08:09.640 a zero or a one. And if we start to 0:08:09.760 --> 0:08:15.560 group these two inputs together, that gives us four potential combos. 0:08:15.640 --> 0:08:19.040 You could have both input A and input B B zero, 0:08:19.600 --> 0:08:22.280 so that's one value. Or you could have both of 0:08:22.280 --> 0:08:25.840 them be one that's a second value. Or you could 0:08:25.840 --> 0:08:29.240 have input A B zero, input B is one that's 0:08:29.280 --> 0:08:32.480 a third value. Or you could have input A B 0:08:32.760 --> 0:08:36.960 one and input B is zero that's your fourth value. 0:08:37.320 --> 0:08:42.000 So four possible combinations zero, zero, zero, one, one zero 0:08:42.400 --> 0:08:45.600 or one one. Now, those are the basics when we 0:08:45.679 --> 0:08:48.720 come back. We're gonna talk about the different kinds of 0:08:48.840 --> 0:08:51.800 logic gates, and we'll build from the most basic to 0:08:52.160 --> 0:08:55.440 the more complicated. But first let's take this quick break 0:08:55.679 --> 0:09:07.439 to thank our sponsor. We're back, So now we're going 0:09:07.480 --> 0:09:10.079 to talk about logic gates, and the first one up 0:09:10.200 --> 0:09:14.680 is the and logic gate. The and logic gate will 0:09:14.720 --> 0:09:19.280 produce a one result as the output only if both 0:09:19.320 --> 0:09:23.600 inputs are also one. So if input A is one, 0:09:23.679 --> 0:09:26.840 an input B is one, then the output is also one. 0:09:27.440 --> 0:09:31.480 Any other combination, whether it's zero, zero, zero, one, or 0:09:31.520 --> 0:09:36.000 one zero, will have an output of zero. So an 0:09:36.040 --> 0:09:39.000 and gate will produce a one if both inputs are 0:09:39.120 --> 0:09:42.800 also one. Next up, we've got the or gate. This 0:09:42.840 --> 0:09:46.000 one will produce a zero output if both inputs are 0:09:46.040 --> 0:09:50.480 also zero, so any other combination will create a one output. 0:09:50.520 --> 0:09:52.960 It's kind of the opposite of the AND gate in 0:09:53.040 --> 0:09:57.280 many ways. Then we have the exclusive or, which is 0:09:57.320 --> 0:10:00.480 agreed not to date other people. I'm sorry, that's the 0:10:00.559 --> 0:10:06.679 nighttime advil talking. The exclusive or x or produces a 0:10:06.800 --> 0:10:09.840 one only if one input is a one and the 0:10:09.880 --> 0:10:12.120 other one is a zero. So if you have one, 0:10:12.240 --> 0:10:15.920 zero or zero, one is the inputs that produces a 0:10:16.000 --> 0:10:19.600 one output. The zero zero and one one inputs would 0:10:19.600 --> 0:10:23.640 produce a zero output. I know this starts getting confusing, 0:10:23.679 --> 0:10:26.600 but this is just for the purposes of explaining the 0:10:26.640 --> 0:10:29.480 different types of logic gates. Next up, we've got the 0:10:29.520 --> 0:10:33.320 logical inverter. So a logic inverter is someone who stands 0:10:33.360 --> 0:10:36.600 mister spot on his head. No, actually no, it's a 0:10:36.640 --> 0:10:40.600 not git and this only has a single input. So 0:10:40.640 --> 0:10:42.640 it's one of those exceptions I was talking about a 0:10:42.679 --> 0:10:45.640 few moments ago. So an inverter does exactly what you 0:10:45.640 --> 0:10:48.920 would expect. It produces an output that's the opposite of 0:10:48.960 --> 0:10:51.440 the input. So if you have a one coming into 0:10:51.520 --> 0:10:55.559 a not git, a zero is coming out, or vice versa. 0:10:56.400 --> 0:10:58.240 Now we're going to get into a few gates that 0:10:58.280 --> 0:11:01.040 combine some of the more simple verse into something a 0:11:01.080 --> 0:11:05.160 little more sophisticated. So first up, we've got the nand gate, 0:11:05.400 --> 0:11:09.679 the NA in D gate. This behaves as if it 0:11:09.880 --> 0:11:13.560 is an and gate immediately followed by a not gate. 0:11:13.760 --> 0:11:17.079 So the nand gate will create a zero output only 0:11:17.520 --> 0:11:21.440 if both inputs are one, so one one creates a 0:11:21.559 --> 0:11:25.800 zero output. Any other combination would produce a one output. 0:11:26.559 --> 0:11:29.640 Then we have the nore gate, which is an or 0:11:29.760 --> 0:11:33.160 gate followed by an inverter. It will only produce a 0:11:33.200 --> 0:11:36.960 one if both inputs are zero, So zero zero creates 0:11:36.960 --> 0:11:40.840 a one output. Every other combination creates a zero output. 0:11:41.360 --> 0:11:45.280 Now let's go crazy Broadway style. We got the exclusive 0:11:45.520 --> 0:11:49.280 nore or x nore gate, which will produce an output 0:11:49.360 --> 0:11:53.280 of one if both inputs are the same. So a 0:11:53.360 --> 0:11:56.959 zero zero input will create a one output, but then 0:11:57.000 --> 0:12:00.760 so will a one one input. Now a one zero 0:12:00.880 --> 0:12:03.400 or a zero one input that would create a zero. 0:12:03.840 --> 0:12:06.240 So yes, I know that sounded like a lot of 0:12:06.320 --> 0:12:09.079 zeros and ones, but that's what we've got to work with. 0:12:09.679 --> 0:12:12.880 And these logic gates are what make up digital circuits. 0:12:13.000 --> 0:12:16.360 You can combine them in all sorts of different configurations, 0:12:16.760 --> 0:12:19.360 with the only real limit being that we are talking 0:12:19.400 --> 0:12:22.800 about physical structures producing these outputs, right, we are talking 0:12:22.800 --> 0:12:27.600 about actual transistors and resistors. So eventually you do start 0:12:27.600 --> 0:12:30.440 to run out of physical space. So they do take 0:12:30.520 --> 0:12:33.199 up space, very little space because these are very very 0:12:33.280 --> 0:12:35.960 very tiny components, but they do take up space. You 0:12:36.000 --> 0:12:39.280 also run into issues like how much heat you're producing 0:12:39.320 --> 0:12:42.520 when you're providing power to the circuit, so that can 0:12:42.600 --> 0:12:46.439 also be a limiting factor, but otherwise you can get 0:12:46.480 --> 0:12:50.720 into lots of complex orientations and configurations. Now, the cool 0:12:50.760 --> 0:12:53.600 thing about this is you could actually write out the 0:12:53.640 --> 0:12:57.200 string of logic gates that your circuits follow. Though you 0:12:57.400 --> 0:13:00.680 would need an awful lot of paper to do anything 0:13:00.880 --> 0:13:04.080 like a modern circuit, you could do it, however. The 0:13:04.120 --> 0:13:07.679 point is that logic gates represent specific rules, and these 0:13:07.760 --> 0:13:11.680 rules determine the output produced based upon the input received. 0:13:11.720 --> 0:13:16.120 And that's the very basic foundation of digital computers. Though 0:13:16.120 --> 0:13:18.959 obviously it gets a lot more complicated from there, but 0:13:19.040 --> 0:13:20.960 that's something I'll just have to tackle on a day 0:13:21.200 --> 0:13:24.240 when I'm not on ADVILPM, which is not a sponsor, 0:13:24.400 --> 0:13:27.079 I should add, it's just the reason this episode turned 0:13:27.120 --> 0:13:32.600 out the way it did, so my apologies on that one. Anyway, 0:13:33.320 --> 0:13:36.760 that's the basics of logic gates. You can get a 0:13:36.800 --> 0:13:39.280 lot more detailed, as I said, and I know it 0:13:39.320 --> 0:13:42.360 gets really confusing hearing all those ones and zeros. I 0:13:42.360 --> 0:13:45.760 recommend looking up truth tables for different logic gates so 0:13:45.800 --> 0:13:48.000 that you can get a better understanding. It helps me, 0:13:48.200 --> 0:13:51.680 at least when I'm able to see visualizations of this 0:13:51.800 --> 0:13:55.079 in various charts, and that lets me get a better 0:13:55.240 --> 0:13:58.280 understanding of what output you're going to get based upon 0:13:58.320 --> 0:14:01.400 the input going in. So yeah, this is like the 0:14:01.440 --> 0:14:05.760 core foundation of processing. So you combine that with the 0:14:06.000 --> 0:14:10.400 element of binary information where your values can either be 0:14:10.440 --> 0:14:13.319 a zero or one. Then you start grouping bits together 0:14:13.440 --> 0:14:18.280 to make more meaningful representations of info. Couple that with 0:14:18.440 --> 0:14:21.560 the process of logic gates, and you start to see 0:14:21.600 --> 0:14:26.640 how computers actually start physically handle this information in the 0:14:26.680 --> 0:14:31.600 form of voltages. It's really incredible, like when you start 0:14:31.600 --> 0:14:34.920 to break it down, because we deal with such an 0:14:35.000 --> 0:14:39.240 abstraction of what computers are doing when we're running any program, right, 0:14:39.280 --> 0:14:42.080 We're just focusing on whatever the program does. We're not 0:14:42.120 --> 0:14:46.280 necessarily thinking what is going on at the circuit level 0:14:46.640 --> 0:14:50.280 to make this happen. Well, logic gates are really the 0:14:50.760 --> 0:14:54.880 basis for that. So I hope this was interesting. I'm 0:14:54.920 --> 0:14:59.800 sure it was at least cringe worthy and maybe in 0:14:59.840 --> 0:15:04.880 a retaining as well due to my aduled state thanks 0:15:04.920 --> 0:15:08.240 to the nighttime medication I accidentally took. And it's still 0:15:08.280 --> 0:15:10.680 doing a number on me, y'all. I've had two full 0:15:10.680 --> 0:15:15.080 cups of coffee to push through this, So blame my 0:15:15.720 --> 0:15:21.200 foolish on grabbing the first headache medicine that I wasn't 0:15:21.240 --> 0:15:23.720 within reach for me to deal with my headache. That's 0:15:23.760 --> 0:15:26.200 the reason. All right, We've got a couple more new 0:15:26.240 --> 0:15:30.400 episodes this week before we get into rerun territory. I've 0:15:30.400 --> 0:15:33.480 got a new episode for tomorrow and for Wednesday, so 0:15:33.880 --> 0:15:35.760 hope you enjoy those. They will also be on the 0:15:35.760 --> 0:15:39.320 shorter side, which was necessary for me to be able 0:15:39.360 --> 0:15:41.880 to get everything done before I headed off on vacation. 0:15:42.600 --> 0:15:46.040 And I hope you are all well. I hope I'm 0:15:46.040 --> 0:15:49.040 well right now. I should be kind of leaning back 0:15:49.080 --> 0:15:53.480 in a hammock in the Blue Ridge Mountains somewhere hopefully 0:15:53.560 --> 0:15:57.040 at this point, unless the weather's terrible, which is probably 0:15:57.040 --> 0:15:59.920 will be, and that case, I'll just be inside watching 0:16:00.080 --> 0:16:02.840 the rain. Either way sounds good to me. And I 0:16:02.880 --> 0:16:12.280 will talk to you again really soon. Tech Stuff is 0:16:12.320 --> 0:16:16.840 an iHeartRadio production. For more podcasts from iHeartRadio, visit the 0:16:16.880 --> 0:16:20.520 iHeartRadio app, Apple Podcasts, or wherever you listen to your 0:16:20.560 --> 0:16:21.280 favorite shows.