WEBVTT 00:00:01.320 --> 00:00:03.020 You know, when you think about the computers 00:00:03.020 --> 00:00:05.179 running our world, you probably picture like 00:00:05.179 --> 00:00:08.339 absolute precision, right? Ones and zeros. Every 00:00:08.339 --> 00:00:11.740 single detail, meticulously calculated, mapped 00:00:11.740 --> 00:00:14.990 out, and accounted for. Right. Yeah. It definitely 00:00:14.990 --> 00:00:17.850 feels comforting to assume that underneath the 00:00:17.850 --> 00:00:20.690 glass screens of our devices, there's this rigid 00:00:20.690 --> 00:00:23.989 binary foundation, a place where nothing is left 00:00:23.989 --> 00:00:26.410 to chance, you know, a perfectly ordered digital 00:00:26.410 --> 00:00:28.370 universe. Yeah, exactly. But then you actually 00:00:28.370 --> 00:00:30.510 peek under the hood of digital logic design and 00:00:30.510 --> 00:00:32.810 suddenly that perfection starts to look a lot 00:00:32.810 --> 00:00:35.829 more like, well, selective blindness. Selective 00:00:35.829 --> 00:00:38.109 blindness. I like that. Right. Because they were 00:00:38.109 --> 00:00:40.810 intentionally ignoring information just to save 00:00:40.810 --> 00:00:44.140 power and space. And the craziest part? that 00:00:44.140 --> 00:00:47.179 intentional ignorance is exactly what makes our 00:00:47.179 --> 00:00:49.920 most advanced machines vulnerable to chaotic 00:00:49.920 --> 00:00:52.140 real -world phenomena. Oh, absolutely. Things 00:00:52.140 --> 00:00:55.179 like cosmic rays. Literally cosmic rays. So welcome 00:00:55.179 --> 00:00:57.520 to the Deep Dive. Today we're exploring a dense, 00:00:57.780 --> 00:00:59.880 highly technical concept in digital logic called 00:00:59.880 --> 00:01:02.600 the Don't Care Term. It's a fundamental tension 00:01:02.600 --> 00:01:05.659 in computer science really. Engineers are constantly 00:01:05.659 --> 00:01:10.340 battling between elegant, optimized theory and 00:01:10.340 --> 00:01:13.519 the messy, unpredictable physical reality we 00:01:13.519 --> 00:01:15.840 actually live in. And that's our mission today. 00:01:16.359 --> 00:01:18.459 We are going to break down how digital systems 00:01:18.459 --> 00:01:21.519 rely on these blind spots to run faster and cheaper. 00:01:21.689 --> 00:01:24.090 Because whether you are a programmer or just, 00:01:24.090 --> 00:01:25.930 you know, someone reading this on a digital screen, 00:01:26.670 --> 00:01:29.409 your devices are actively making don't care decisions 00:01:29.409 --> 00:01:31.409 right now to save power. They absolutely are. 00:01:31.430 --> 00:01:33.450 It's happening constantly. But we're also going 00:01:33.450 --> 00:01:36.590 to look at what happens when the physical universe 00:01:36.590 --> 00:01:40.090 forces those systems to care and to guide you 00:01:40.090 --> 00:01:41.950 through this kind of counterintuitive logic. 00:01:42.329 --> 00:01:44.909 I've got our expert here. Thanks, yeah. To really 00:01:44.909 --> 00:01:47.010 grasp how these systems break down, we first 00:01:47.010 --> 00:01:48.750 have to look at how they're built to ignore things 00:01:48.750 --> 00:01:51.170 in the first place. Right. So at the very bottom 00:01:51.170 --> 00:01:53.650 of computing, you have Boolean functions. That's 00:01:53.650 --> 00:01:55.950 the underlying math of ones and zeros that makes 00:01:55.950 --> 00:01:58.969 logic gates work. And within that math, engineers 00:01:58.969 --> 00:02:01.530 use two distinct concepts. OK, what's the first 00:02:01.530 --> 00:02:05.390 one? First is the don't care term. This is simply 00:02:05.390 --> 00:02:07.790 an input sequence where the designer decides 00:02:07.790 --> 00:02:11.870 the output of the function. Just doesn't matter. 00:02:12.050 --> 00:02:14.370 It's just a giant shrug from the system. Pretty 00:02:14.370 --> 00:02:17.349 much. And its sibling concept is the can't happen 00:02:17.349 --> 00:02:20.150 term. This is an input that the system assumes 00:02:20.150 --> 00:02:22.770 will literally never occur in the real world. 00:02:23.030 --> 00:02:25.150 Never ever. Right. And when you dig into the 00:02:25.150 --> 00:02:28.669 engineering history, you see decades of logic 00:02:28.669 --> 00:02:31.490 designers wrestling with what to even call these 00:02:31.490 --> 00:02:34.050 informational voids. Because don't care is pretty 00:02:34.050 --> 00:02:37.449 informal. Right, exactly. So you'll see historical 00:02:37.449 --> 00:02:40.810 aliases like redundancies, irrelevancies, vacuous 00:02:40.810 --> 00:02:43.270 combinations, and my personal favorite, forbidden 00:02:43.270 --> 00:02:45.870 combinations. Forbidden combinations. That sounds 00:02:45.870 --> 00:02:47.849 like something out of an alchemy textbook, not, 00:02:47.849 --> 00:02:50.150 you know, computer engineering. It really does. 00:02:50.430 --> 00:02:53.569 OK, let's unpack this. Why would a designer whose 00:02:53.569 --> 00:02:56.569 entire job is to build a precise, predictable 00:02:56.569 --> 00:03:00.419 machine purposely introduce irrelevancies. Is 00:03:00.419 --> 00:03:01.840 this like building a house with a blueprint, 00:03:02.120 --> 00:03:04.020 but since you know nobody will ever walk on the 00:03:04.020 --> 00:03:06.139 ceiling, you don't care about putting carpet 00:03:06.139 --> 00:03:08.039 up there. That's a great way to think about it. 00:03:08.159 --> 00:03:10.680 So by ignoring the ceiling, you just save money 00:03:10.680 --> 00:03:13.319 and time on the overall build. Yes, exactly. 00:03:13.900 --> 00:03:16.439 Just like the ceiling, leaving it undefined is 00:03:16.439 --> 00:03:18.860 an intentional design choice to optimize the 00:03:18.860 --> 00:03:21.780 whole structure. In logic design, it's all about 00:03:21.780 --> 00:03:24.620 minimization. Minimization, meaning making things 00:03:24.620 --> 00:03:27.360 smaller. Making them smaller, simpler, faster. 00:03:27.800 --> 00:03:30.419 Every single logic gate you add to a circuit 00:03:30.419 --> 00:03:33.780 requires physical space on a silicon chip. It 00:03:33.780 --> 00:03:37.060 requires manufacturing materials. And crucially, 00:03:37.300 --> 00:03:39.699 it requires electricity to run, which generates 00:03:39.699 --> 00:03:42.419 heat. Right. And heat is the enemy of electronics. 00:03:42.659 --> 00:03:45.280 Exactly. So by treating certain complex conditions 00:03:45.280 --> 00:03:48.300 as don't cares, the designer doesn't have to 00:03:48.300 --> 00:03:50.819 wire a specific physical path for them. They 00:03:50.819 --> 00:03:52.719 just leave it blank. Well, they do better than 00:03:52.719 --> 00:03:54.780 leave it blank. They strategically assign it 00:03:54.780 --> 00:03:57.360 at one or zero based on whatever makes the rest 00:03:57.360 --> 00:03:59.639 of the circuit simpler. Wait, how do they decide 00:03:59.639 --> 00:04:02.849 that? Engineers use graphical methods like Karnavatch 00:04:02.849 --> 00:04:05.530 maps to do this, or even algebraic methods like 00:04:05.530 --> 00:04:07.629 the Quine -McCluskey algorithm. Let's stick to 00:04:07.629 --> 00:04:11.330 the visual one. The map. Sure. Imagine a grid 00:04:11.330 --> 00:04:14.409 on a piece of paper filled with ones and zeros 00:04:14.409 --> 00:04:16.629 representing the desired outputs of a circuit. 00:04:17.000 --> 00:04:19.959 To minimize the physical gates, engineers look 00:04:19.959 --> 00:04:22.079 for groups of ones they can circle together. 00:04:22.240 --> 00:04:24.199 Like finding a word in a word search puzzle. 00:04:24.360 --> 00:04:26.759 Right. And the larger the circle they can draw, 00:04:26.899 --> 00:04:29.319 the simpler the resulting algebraic equation 00:04:29.319 --> 00:04:34.000 becomes, which means fewer physical wires. Now, 00:04:34.480 --> 00:04:36.920 if you have a can't happen state, a square on 00:04:36.920 --> 00:04:38.980 that grid that you know will never be triggered, 00:04:39.420 --> 00:04:42.319 you can drop a don't care wild card into that 00:04:42.319 --> 00:04:44.100 square. Just pretend it's whatever you need it 00:04:44.100 --> 00:04:46.500 to be. Exactly. If treating that wild card as 00:04:46.439 --> 00:04:49.100 So one allows you to draw a massive circle connecting 00:04:49.100 --> 00:04:51.860 other real ones. You do it. You've just mathematically 00:04:51.860 --> 00:04:54.939 squeezed the waste out of the design. Wow. OK, 00:04:55.060 --> 00:04:57.180 but hasn't this always been the goal? It has. 00:04:57.420 --> 00:04:59.819 But translating that theory into physical reality 00:04:59.819 --> 00:05:02.899 took time. Back in 1958, a mathematician named 00:05:02.899 --> 00:05:05.439 Seymour Ginsburg actually proved something really 00:05:05.439 --> 00:05:07.199 frustrating for engineers. What did he prove? 00:05:07.389 --> 00:05:10.230 He proved that minimizing the states of a machine 00:05:10.230 --> 00:05:12.730 using these don't care conditions didn't necessarily 00:05:12.730 --> 00:05:15.129 guarantee you were minimizing the actual physical 00:05:15.129 --> 00:05:18.310 logic elements on the board. Wait, why not? If 00:05:18.310 --> 00:05:20.670 you simplify the math, shouldn't the physical 00:05:20.670 --> 00:05:23.600 machine automatically be simpler? Not necessarily. 00:05:23.959 --> 00:05:26.220 Ginsburg showed that sometimes combining states 00:05:26.220 --> 00:05:28.779 mathematically forces you to use more complex 00:05:28.779 --> 00:05:31.699 physical wiring to write the signals between 00:05:31.699 --> 00:05:35.180 those newly combined states. Oh, so the abstract 00:05:35.180 --> 00:05:37.920 math doesn't perfectly match the physical silicon. 00:05:38.000 --> 00:05:41.720 Right. And the real problem was, in 1958, they 00:05:41.720 --> 00:05:44.379 didn't have the computational power to test the 00:05:44.379 --> 00:05:46.899 millions of combinations required to perfectly 00:05:46.899 --> 00:05:49.899 align the abstract state minimization with the 00:05:49.899 --> 00:05:52.490 physical logic minimization. computationally 00:05:52.490 --> 00:05:54.649 impractical for large systems at the time. Exactly. 00:05:54.930 --> 00:05:57.149 They were mapping out the philosophy of intentional 00:05:57.149 --> 00:05:59.490 ignorance long before they had the supercomputers 00:05:59.490 --> 00:06:02.029 needed to fully exploit it. So to see how this 00:06:02.029 --> 00:06:04.370 works in the real world today, let's look at 00:06:04.370 --> 00:06:07.009 how computers handle basic human numbers. We 00:06:07.009 --> 00:06:10.069 operate on a base -10 system, right? Zero through 00:06:10.069 --> 00:06:13.050 nine. But computers operate in binary ones and 00:06:13.050 --> 00:06:15.949 zeros. So engineers use something called binary 00:06:15.949 --> 00:06:19.509 coded decimal or BCD to bridge the gap. And that 00:06:19.509 --> 00:06:22.269 translation creates a fascinating mathematical 00:06:22.269 --> 00:06:25.189 leftover. How so? Well, to represent the human 00:06:25.189 --> 00:06:29.029 number 9, a computer needs a 4 -bit binary sequence, 00:06:29.509 --> 00:06:33.410 specifically 1001. But a 4 -bit sequence can 00:06:33.410 --> 00:06:36.769 actually hold up to 16 different values, from 00:06:36.769 --> 00:06:40.129 0 all the way up to 15. Which means, if you are 00:06:40.129 --> 00:06:43.079 only ever counting from 0 to 9, Those binary 00:06:43.079 --> 00:06:47.220 values for 10, 11, 12, 13, 14, and 15 will absolutely 00:06:47.220 --> 00:06:49.379 never be used. Right. This system assumes they 00:06:49.379 --> 00:06:52.120 are impossible. And there's a specific engineering 00:06:52.120 --> 00:06:55.019 term for these leftover impossible inputs, right? 00:06:55.699 --> 00:06:58.360 Pseudotetraids. Yes, pseudotetraids. The term 00:06:58.360 --> 00:07:00.360 itself highlights their phantom nature. They 00:07:00.360 --> 00:07:02.800 were valid binary combinations that simply have 00:07:02.800 --> 00:07:05.319 no meaning in a decimal context. And designers 00:07:05.319 --> 00:07:07.879 exploit these pseudotetraids aggressively to 00:07:07.879 --> 00:07:10.000 save money. I think the classic example of this 00:07:10.000 --> 00:07:11.959 is the seven segment display. Oh, that's a perfect 00:07:11.959 --> 00:07:14.939 example. Yeah, think of the blocky red digital 00:07:14.939 --> 00:07:17.939 numbers on a bedside alarm clock or like a microwave. 00:07:18.459 --> 00:07:20.980 Each number is made of up to seven little LED 00:07:20.980 --> 00:07:24.600 bars. The logic circuit behind that display has 00:07:24.600 --> 00:07:27.319 to constantly compute when to turn on say the 00:07:27.319 --> 00:07:29.560 lower left bar. And this is where the minimization 00:07:29.560 --> 00:07:31.600 we talked about earlier physically manifests. 00:07:32.040 --> 00:07:34.839 To definitively tell that lower left bar what 00:07:34.839 --> 00:07:37.629 to do, the circuit normally has to check all 00:07:37.629 --> 00:07:40.230 four binary wires. Like it has to ask, are you 00:07:40.230 --> 00:07:43.149 a zero? Are you a one? Are you an eight? Exactly. 00:07:43.370 --> 00:07:45.649 But the designer knows the inputs for 10 through 00:07:45.649 --> 00:07:48.449 15 will never happen. So they just don't bother 00:07:48.449 --> 00:07:50.930 building the complex web of logic gates required 00:07:50.930 --> 00:07:52.949 to check for those higher numbers. They just 00:07:52.949 --> 00:07:55.329 drop those don't care wild cards onto their Karnaugh 00:07:55.329 --> 00:07:57.949 map. Yes. They make an arbitrary mathematical 00:07:57.949 --> 00:08:00.430 choice for those pseudo tetraids, allowing them 00:08:00.430 --> 00:08:03.589 to strip the circuit down to a bare bones algebraic 00:08:03.589 --> 00:08:05.529 equation. And what does that equation look like? 00:08:05.649 --> 00:08:07.870 In the case of that lower or left bar, they reduce 00:08:07.870 --> 00:08:10.569 the logic to simply checking two specific conditions, 00:08:10.750 --> 00:08:13.970 usually written algebraically as A0B plus A0C. 00:08:14.329 --> 00:08:16.689 They bypass checking the other wires entirely. 00:08:17.089 --> 00:08:19.870 Wow. So that physically shrinks the microchip. 00:08:20.149 --> 00:08:22.750 Significantly. They are literally erasing physical 00:08:22.750 --> 00:08:25.149 wires from the manufacturing process just by 00:08:25.149 --> 00:08:27.290 letting the math bleed over into the impossible 00:08:27.290 --> 00:08:30.329 numbers. Exactly. And this isn't just for alarm 00:08:30.329 --> 00:08:33.529 clocks. This exact same shortcut is used in complex 00:08:33.529 --> 00:08:36.279 encoding schemes, too. Right, the source mentioned 00:08:36.279 --> 00:08:40.039 schemes with names like Hertz, Chen Ho, and densely 00:08:40.039 --> 00:08:42.679 packed decimal. Yes, all of them rely on this. 00:08:43.080 --> 00:08:45.679 It also shows up in OLDL hardware with things 00:08:45.679 --> 00:08:48.080 called write -only registers. Oh yeah, the write 00:08:48.080 --> 00:08:50.460 -only registers. That was a direct consequence 00:08:50.460 --> 00:08:53.580 of engineers trading off functionality just to 00:08:53.580 --> 00:08:56.259 reduce the number of logic gates. But that brings 00:08:56.259 --> 00:08:58.759 up a really specific mechanical question that 00:08:58.759 --> 00:09:00.799 I had when reading the source. OK, what is it? 00:09:01.059 --> 00:09:03.940 If you have a write -only register, and you attempt 00:09:03.940 --> 00:09:07.139 to read it, the source says a don't care is read. 00:09:07.860 --> 00:09:09.980 How does a computer actually read a don't care? 00:09:10.539 --> 00:09:12.820 Does it just spit out garbage data to the user 00:09:12.820 --> 00:09:15.490 because it traded functionality for Fewer gates? 00:09:15.730 --> 00:09:18.269 What's fascinating here is that the system literally 00:09:18.269 --> 00:09:20.970 shrugs. It shrugs. Yeah, it provides whatever 00:09:20.970 --> 00:09:23.970 arbitrary output was cheapest to wire because 00:09:23.970 --> 00:09:25.789 you were never supposed to ask it that question. 00:09:26.049 --> 00:09:28.070 You were asking for data from a pathway that 00:09:28.070 --> 00:09:31.490 was intentionally left blank to save a microsenon 00:09:31.490 --> 00:09:34.029 manufacturing. So the physical circuitry just 00:09:34.029 --> 00:09:36.450 like gives you whatever residual electricity 00:09:36.450 --> 00:09:39.370 happens to be there. Basically, yes. OK. But 00:09:39.370 --> 00:09:42.389 before a single wire is ever soldered or a chip 00:09:42.389 --> 00:09:45.179 is printed, engineers have to test this stuff 00:09:45.179 --> 00:09:48.500 on computers. How do they simulate a void of 00:09:48.500 --> 00:09:51.100 information before the hardware is even built? 00:09:51.580 --> 00:09:54.539 Well, in the realm of multi -valued logic systems, 00:09:54.840 --> 00:09:58.529 they introduce the x -value. The x -value. Which 00:09:58.529 --> 00:10:00.889 stands for don't know. Exactly. When engineers 00:10:00.889 --> 00:10:03.029 write the code that will eventually be synthesized 00:10:03.029 --> 00:10:05.490 into physical hardware, they use hardware description 00:10:05.490 --> 00:10:08.090 languages. In Verilog, for example, these unknown 00:10:08.090 --> 00:10:10.669 values are just denoted by the letter X. And 00:10:10.669 --> 00:10:13.509 in another language called VHDL, things get even 00:10:13.509 --> 00:10:16.669 more specific. They use X to mean a forced unknown, 00:10:16.889 --> 00:10:19.629 but they also use the letter W key to represent 00:10:19.629 --> 00:10:22.490 a weak unknown. That distinction is really important 00:10:22.490 --> 00:10:25.769 for simulating real world physics. How so? Well, 00:10:26.070 --> 00:10:29.440 a forced unknown The X happens in a simulation 00:10:29.440 --> 00:10:32.120 if two sources are driving a signal simultaneously, 00:10:32.299 --> 00:10:33.960 like they're basically fighting each other to 00:10:33.960 --> 00:10:37.279 a draw. OK. And the weak unknown? A weak unknown, 00:10:37.480 --> 00:10:40.659 the W -YO, is an undefined signal that isn't 00:10:40.659 --> 00:10:43.500 being actively pushed by a strong power source, 00:10:43.779 --> 00:10:46.500 so it can easily be overridden if a valid zero 00:10:46.500 --> 00:10:49.120 or one comes along. It's the software saying, 00:10:49.480 --> 00:10:53.279 I am confused. This pathway is currently undefined. 00:10:54.279 --> 00:10:56.500 This can also happen if a tiny component called 00:10:56.500 --> 00:10:59.240 a flip -flop hasn't reached a stable output yet, 00:10:59.240 --> 00:11:01.419 right? Right. A flip -flop holds state. It's 00:11:01.419 --> 00:11:03.759 the fundamental building block of computer memory. 00:11:04.139 --> 00:11:06.299 Think of it like a tiny seesaw. It holds a one 00:11:06.299 --> 00:11:08.259 when it's tilted up and a zero when it's down. 00:11:08.460 --> 00:11:10.919 Okay, I'm picturing it. But during a transition, 00:11:11.179 --> 00:11:13.000 that seesaw can balance perfectly in the middle 00:11:13.000 --> 00:11:15.480 for a fraction of a microsecond. In the pure 00:11:15.480 --> 00:11:17.799 math of a simulation software, the program can 00:11:17.799 --> 00:11:19.960 look at that perfectly balanced seesaw and just 00:11:19.960 --> 00:11:22.460 ladle it X. It can just sit there unresolved. 00:11:22.740 --> 00:11:24.679 Here's where it gets really interesting. So in 00:11:24.679 --> 00:11:27.360 the simulation software, X is a literal placeholder 00:11:27.360 --> 00:11:30.700 for confused. But in the real world, the physical 00:11:30.700 --> 00:11:34.720 wire has to hold a voltage. It is forced to pick 00:11:34.720 --> 00:11:38.500 aside a 0 or a 1. Even if it's completely blind 00:11:38.500 --> 00:11:41.059 to what it should be, it can't just hover in 00:11:41.059 --> 00:11:43.539 an X state in physical hardware. This raises 00:11:43.539 --> 00:11:46.059 an important question about the danger of assumptions. 00:11:46.860 --> 00:11:50.059 When a simulation allows an X, a nice, safe, 00:11:50.399 --> 00:11:53.480 undefined placeholder, but reality demands a 00:11:53.480 --> 00:11:57.840 definitive 1 or 0, a dangerous gap opens up between 00:11:57.840 --> 00:12:01.399 theory and physical execution. because the synthesized 00:12:01.399 --> 00:12:04.940 physical hardware's actual value is indeterminable 00:12:04.940 --> 00:12:07.500 from the inputs. Exactly. Which brings us to 00:12:07.500 --> 00:12:10.240 the chaos of the physical universe. Since the 00:12:10.240 --> 00:12:13.220 physical hardware must pick a 1 or a 0, what 00:12:13.220 --> 00:12:15.320 actually happens when the real world forces the 00:12:15.320 --> 00:12:17.539 system into one of those can't happen combinations? 00:12:18.200 --> 00:12:20.399 The forbidden inputs the engineers assumed could 00:12:20.399 --> 00:12:22.639 never happen. Things get truly precarious when 00:12:22.639 --> 00:12:24.259 we look at circuits with feedback. These are 00:12:24.259 --> 00:12:26.580 known as state machines. State machines. Right. 00:12:26.759 --> 00:12:29.220 A state machine depends heavily on its own previous 00:12:29.220 --> 00:12:32.179 outputs and external inputs. It has a memory 00:12:32.179 --> 00:12:34.500 of the state it is currently in. It's like a 00:12:34.500 --> 00:12:36.399 combination lock that remembers the last number 00:12:36.399 --> 00:12:39.379 you spun to. Great analogy. And the environment 00:12:39.379 --> 00:12:43.299 is constantly threatening that memory. The real 00:12:43.299 --> 00:12:45.600 world can accidentally generate these forbidden 00:12:45.600 --> 00:12:48.629 inputs. Like what kind of threats it could be 00:12:48.629 --> 00:12:50.850 a voltage glitch during the circuits power -up 00:12:50.850 --> 00:12:54.190 phase or Random interference from a heat spike. 00:12:54.529 --> 00:12:57.190 It could be electrical noise or incredibly. It 00:12:57.190 --> 00:13:00.590 can be cosmic radiation Wait cosmic radiation. 00:13:00.870 --> 00:13:03.669 So an engineer perfectly designs a state machine 00:13:03.669 --> 00:13:06.370 mathematically proves an input will never occur 00:13:06.370 --> 00:13:10.029 and Then literally a particle from outer space 00:13:10.029 --> 00:13:12.799 hits the computer and throws it into a forbidden 00:13:12.799 --> 00:13:15.019 state. I know it sounds like sci -fi, but yes. 00:13:15.120 --> 00:13:17.039 It's like building an impenetrable bank vault, 00:13:17.360 --> 00:13:19.159 and then a meteor teleports inside of it. That 00:13:19.159 --> 00:13:21.519 is exactly what it's like, and that's why nominally 00:13:21.519 --> 00:13:24.200 can't -happen states are actually deeply dangerous, 00:13:24.519 --> 00:13:27.059 because cosmic rays are high -energy particles 00:13:27.059 --> 00:13:29.100 constantly raining down on Earth. And if one 00:13:29.100 --> 00:13:31.679 hits the chip perfectly... It can inject a microscopic 00:13:31.679 --> 00:13:34.679 charge. It physically flips a single bit from 00:13:34.679 --> 00:13:37.500 a zero to a one. Which means the machine is suddenly 00:13:37.500 --> 00:13:39.980 experiencing an input that the designer guaranteed 00:13:39.980 --> 00:13:43.600 was impossible. Right. Suddenly, your combination 00:13:43.600 --> 00:13:45.980 lock thinks it is set to a number that isn't 00:13:45.980 --> 00:13:48.799 even painted on the dial. And because the logic 00:13:48.799 --> 00:13:51.320 was minimized to save space, there's no pathway 00:13:51.320 --> 00:13:53.379 instructing the lock on what to do. The results 00:13:53.379 --> 00:13:55.080 of this are catastrophic, right? Completely. 00:13:55.360 --> 00:13:57.600 In computer engineering, this is called a hardware 00:13:57.600 --> 00:14:00.919 lockup or a soft error. Your device essentially 00:14:00.919 --> 00:14:04.009 freezes into a coma. Because it enters what the 00:14:04.009 --> 00:14:06.529 source called the walled garden of states. The 00:14:06.529 --> 00:14:08.929 walled garden. Which usually sounds pleasant, 00:14:09.169 --> 00:14:11.929 but here it is a scenario where the machine is 00:14:11.929 --> 00:14:15.669 stuck between can't happen states with absolutely 00:14:15.669 --> 00:14:18.590 no combination of inputs that can exit it back 00:14:18.590 --> 00:14:21.330 into normal operation. Because they used don't 00:14:21.330 --> 00:14:23.649 care logic to minimize the circuitry, they didn't 00:14:23.649 --> 00:14:26.320 build an exit. The cosmic ray pushes the machine 00:14:26.320 --> 00:14:28.840 into the walled garden and it is entirely trapped. 00:14:29.000 --> 00:14:30.980 Just bouncing around inside the forbidden logic 00:14:30.980 --> 00:14:33.679 loop forever? Exactly. Entirely unresponsive. 00:14:33.860 --> 00:14:36.860 So if a random burst of heat or cosmic radiation 00:14:36.860 --> 00:14:39.299 can permanently trap our technology in a walled 00:14:39.299 --> 00:14:41.940 garden, how do engineers prevent our devices 00:14:41.940 --> 00:14:44.500 from instantly becoming expensive paperweights? 00:14:44.840 --> 00:14:47.440 Well, they have to design safety nets. There 00:14:47.440 --> 00:14:50.019 are three main mitigation strategies designers 00:14:50.019 --> 00:14:52.580 must employ for state machines. What's option 00:14:52.580 --> 00:14:55.320 one? Option one is the brute force approach. 00:14:55.899 --> 00:14:58.960 They must take extra physical steps to ensure 00:14:58.960 --> 00:15:02.559 the forbidden combinations are truly made. Can't 00:15:02.559 --> 00:15:05.480 happen. But doesn't that mean heavily shielding 00:15:05.480 --> 00:15:08.019 the system? Wouldn't that completely ruin the 00:15:08.019 --> 00:15:10.820 whole point of minimizing the circuit to save 00:15:10.820 --> 00:15:13.840 money and space? It absolutely does. It's a massive 00:15:13.840 --> 00:15:16.379 trade off, usually reserved for things like aerospace 00:15:16.379 --> 00:15:19.039 or medical devices. Where failure is just not 00:15:19.039 --> 00:15:21.559 an option. Right. So for everyday electronics, 00:15:21.860 --> 00:15:24.620 option two is more common, making them transitory. 00:15:25.059 --> 00:15:27.659 How does a transitory state work? The designer 00:15:27.659 --> 00:15:30.879 explicitly wires the walled garden so that it 00:15:30.879 --> 00:15:33.779 has a trap door. If the machine enters a forbidden 00:15:33.779 --> 00:15:36.620 state, the very next tick of the clock will automatically 00:15:36.620 --> 00:15:39.059 lead it back to a normal operational state. OK, 00:15:39.059 --> 00:15:41.320 so it auto -fleshes the system. Exactly. The 00:15:41.320 --> 00:15:43.539 user might experience a tiny glitch, but it won't 00:15:43.539 --> 00:15:46.519 permanently lock up. That makes sense. But then 00:15:46.519 --> 00:15:49.240 there is option three, which is creating a don't 00:15:49.240 --> 00:15:52.120 care alarm to indicate an emergency state for 00:15:52.120 --> 00:15:55.100 air detection. Yes, the don't care alarm. And 00:15:55.100 --> 00:15:57.019 I have to call out this phrase from the source, 00:15:57.220 --> 00:16:01.139 a don't care alarm. Isn't that the ultimate oxymoron? 00:16:01.519 --> 00:16:04.240 How do you mean? Well, if you are taking the 00:16:04.240 --> 00:16:07.899 time to design a specific emergency protocol 00:16:07.899 --> 00:16:11.419 and an alarm for it, you explicitly do care. 00:16:11.679 --> 00:16:14.659 If we connect this to the bigger picture. That 00:16:14.659 --> 00:16:17.700 is the beautiful irony of digital design. Engineers 00:16:17.700 --> 00:16:20.379 start out using don't cares to save time, space, 00:16:20.500 --> 00:16:22.740 and money. They want to strip the system down 00:16:22.740 --> 00:16:25.679 to its absolute most efficient form. Right. But 00:16:25.679 --> 00:16:28.120 because the physical world is inherently chaotic, 00:16:28.539 --> 00:16:30.120 they eventually have to spend time and money 00:16:30.120 --> 00:16:32.139 building alarms just to protect the system from 00:16:32.139 --> 00:16:34.919 its own optimized ignorance. Wow. They optimize 00:16:34.919 --> 00:16:36.940 themselves into a corner and then have to build 00:16:36.940 --> 00:16:39.419 a fire alarm inside that corner. That's the reality 00:16:39.419 --> 00:16:41.659 of bridging abstract math with physical hardware. 00:16:41.879 --> 00:16:44.700 It really reframes how you look at the devices 00:16:44.700 --> 00:16:46.799 around us. We started this deep dive looking 00:16:46.799 --> 00:16:48.980 at an obscure trick that don't care term. We 00:16:48.980 --> 00:16:51.720 saw how things like Karnaugh maps allow for brilliant, 00:16:52.440 --> 00:16:54.519 elegant minimization. Like stripping down the 00:16:54.519 --> 00:16:58.460 seventh segment displays. Exactly. But we also 00:16:58.460 --> 00:17:00.620 saw that the physical universe doesn't respect 00:17:00.620 --> 00:17:03.360 our mathematical boundaries. The physical realities 00:17:03.360 --> 00:17:07.539 of X values heat and cosmic radiation force engineers 00:17:07.539 --> 00:17:10.720 to build safety nets like don't care alarms to 00:17:10.720 --> 00:17:13.539 prevent permanent hardware lockups. It's a constant 00:17:13.539 --> 00:17:16.460 invisible negotiation happening millions of times 00:17:16.460 --> 00:17:18.420 a second inside your phone. Which leaves you 00:17:18.420 --> 00:17:20.579 with something to chew on. We build our most 00:17:20.579 --> 00:17:23.200 advanced systems to efficiently ignore the impossible. 00:17:23.819 --> 00:17:26.059 But since the physical universe guarantees that 00:17:26.059 --> 00:17:28.480 the impossible like a random cosmic ray will 00:17:28.480 --> 00:17:31.160 eventually happen, our most optimized digital 00:17:31.160 --> 00:17:34.000 systems inherently are most fragile. It's a great 00:17:34.000 --> 00:17:35.640 question. Think about that the next time your 00:17:35.640 --> 00:17:38.420 screen freezes for no apparent reason. Thank 00:17:38.420 --> 00:17:40.359 you for joining us on this deep dive and keep 00:17:40.359 --> 00:17:41.500 asking the big questions.