WEBVTT 00:00.760 --> 00:01.600 Hello everyone. 00:01.880 --> 00:07.000 Welcome back to another session in our course on computer organization and low level computing. 00:07.240 --> 00:12.400 Now in this lecture, we are diving deep into two of the most powerful and widely used logic gates in 00:12.400 --> 00:18.840 digital electronics, which is Nand, Nand, and Nor gates. 00:19.240 --> 00:24.120 Now, by the end of this lecture, you will not only know what these gates are, but also why they matter 00:24.120 --> 00:25.040 so much. 00:25.240 --> 00:33.440 So much, in fact, that you can build any other logic gate using just Nand, these Nans or just N or 00:34.200 --> 00:34.880 Nors. 00:35.240 --> 00:38.600 Now that's why they are called the Universal Gates. 00:38.640 --> 00:42.080 Now this lecture is designed to be detailed and beginner friendly. 00:42.080 --> 00:47.720 I will explain every symbol, operation, and logic step along the way. 00:48.840 --> 00:51.920 Now what are logic gates? 00:51.960 --> 00:58.760 Logic gates are tiny electronic components that perform basic logical functions, just like you do in 00:58.760 --> 01:00.880 a math or when making decisions. 01:00.880 --> 01:08.640 Let's say if it is raining then and no. 01:08.640 --> 01:12.800 Yeah, if it is raining and I am tired. 01:17.840 --> 01:20.880 Then do not go out. 01:23.760 --> 01:28.320 So that's basically a logic gate. 01:28.680 --> 01:39.440 Now each gate takes one or more input, which is uh represented as zeros or ones, which is off or on 01:39.640 --> 01:42.040 and produces a single output. 01:42.080 --> 01:48.240 It is either zero and one if not going out counts as zero. 01:48.280 --> 01:50.120 Yeah, we can count as zero as well. 01:51.480 --> 01:52.160 And yeah. 01:52.520 --> 01:59.480 And most logic gates are built using electronic switches called Transistors. 02:04.800 --> 02:06.760 And here's the thing about them. 02:06.920 --> 02:12.880 In many cases, transistors flip the logic of a signal. 02:13.320 --> 02:22.120 So this means when you input a one, you might get zero as an output. 02:22.560 --> 02:31.120 And when you input a zero, you might get a one instead. 02:32.160 --> 02:39.920 Now this inversion behavior is the foundation for gates like Nand and Nor. 02:40.120 --> 02:42.640 And we will see exactly how that works next. 02:47.560 --> 02:51.480 So what is a Nand gate or Nand gate. 02:52.440 --> 02:58.040 Now let's break the break down the name first here because it will make so much sense. 02:58.910 --> 03:08.870 So none here basically means not plus and that is as simple as it gets. 03:09.510 --> 03:16.310 It means take the output of an and gate and then flip it using a not gate. 03:17.470 --> 03:26.070 So let's recap the and gate because we have learned that learned the and and or gates and the other 03:26.070 --> 03:27.630 gates in previous lectures. 03:28.150 --> 03:30.670 So what how the Nand gate worked. 03:30.710 --> 03:34.550 Remember we have A and B input. 03:35.830 --> 03:37.430 We give it to. 03:41.110 --> 03:43.670 A b. 03:43.710 --> 03:46.430 And now this is and operator you see. 03:53.990 --> 03:56.310 So let's start the equations. 03:56.510 --> 03:58.470 So zero zero. 03:58.510 --> 04:00.110 If A is zero, P is zero. 04:00.390 --> 04:01.670 We will get zero. 04:01.950 --> 04:06.270 If A is zero, B is one, we will get zero. 04:06.630 --> 04:10.150 If A is one, B is zero, we will get zero. 04:10.150 --> 04:14.830 And if A is one and B is one, we will get one. 04:23.710 --> 04:28.150 Now this symbol you see here is the and symbol. 04:28.950 --> 04:34.430 Uh, like in math it is um also called a the logical conjunction. 04:34.950 --> 04:37.190 So now let's add a not gate. 04:37.550 --> 04:41.110 Remember a not gate simply flips the result. 04:41.110 --> 04:43.830 If the result is one it becomes zero. 04:43.870 --> 04:45.990 If it was zero, it becomes one. 04:46.190 --> 04:53.510 So when you combine and and z naught you get an A and D. 04:53.830 --> 05:02.790 So Nand gate outputs zero if both inputs are one and one, in all other cases, just the opposite of 05:02.830 --> 05:04.070 and right. 05:04.470 --> 05:08.510 So let's actually write this Nand here. 05:09.470 --> 05:17.070 So this A and B this is so easy right. 05:17.550 --> 05:19.470 So here is a symbol. 05:19.670 --> 05:26.750 This this is a small curved line means not or logical negation. 05:27.150 --> 05:29.550 So this is what not. 05:30.030 --> 05:33.870 And this is basically and right this is and. 05:36.990 --> 05:46.030 And you can also see this written as this ternary operator and this symbol in some books or just Nand 05:47.710 --> 05:48.950 and equation here. 05:54.110 --> 05:56.910 So Remember. 05:59.430 --> 06:02.510 We had what now? 06:02.750 --> 06:07.910 Since it is zero here, we will get one, one, one and zero. 06:08.150 --> 06:08.790 That's it. 06:10.110 --> 06:14.390 Uh, so we get zero if both inputs are one. 06:16.910 --> 06:20.470 We get one in all other cases. 06:34.190 --> 06:43.710 So a Nand gate looks like a regular Nand gate, which is flat packed D shape, but with a small circle 06:43.710 --> 06:44.590 at the output. 06:45.030 --> 06:53.070 So that little circle means here basically, or, uh, inversion or not. 06:55.670 --> 06:56.150 So. 06:58.670 --> 07:01.070 What about this nor gate here? 07:01.230 --> 07:04.110 So this is also very interesting. 07:04.150 --> 07:05.190 Interesting here. 07:05.630 --> 07:16.270 Now just like Nand is not plus and and nor gate as you know is just not or not or. 07:16.990 --> 07:18.510 So not plus or. 07:25.150 --> 07:29.190 So let's write our note or diagram. 07:31.830 --> 07:34.350 Or instead we can do like this. 07:35.030 --> 07:38.910 We have what a and b. 07:41.270 --> 07:49.470 But this is and as you remember from as you learned from this previous lecture, this is what or. 07:52.430 --> 07:55.260 So in or here we have zero and zero. 07:55.300 --> 07:56.020 We get what? 07:56.900 --> 07:57.540 Zero? 07:58.220 --> 07:59.540 We have zero and one. 07:59.540 --> 08:00.420 We get one. 08:01.140 --> 08:02.540 We have one and zero. 08:02.540 --> 08:07.500 Since we have ones here, we got one, one and one. 08:07.540 --> 08:10.620 Of course here we can get one here. 08:12.060 --> 08:15.620 So this symbol is the or symbol. 08:16.380 --> 08:20.380 In mathematics this is called the logical disjunction. 08:21.180 --> 08:25.140 Now as before we flip the output using a Not gate. 08:25.700 --> 08:36.900 So a Nor gate outputs one only if both inputs are zero and zero in all other cases. 08:37.820 --> 08:41.460 So how do we write the Nor gate? 08:42.500 --> 08:44.100 Again note. 08:47.060 --> 08:48.180 Small curved line. 08:51.260 --> 08:51.780 And. 08:54.060 --> 08:54.420 A. 09:00.180 --> 09:01.340 Or B. 09:01.620 --> 09:02.220 That's it. 09:03.020 --> 09:13.740 So what we will get here one if the both inputs are zero and zero in all other cases. 09:15.940 --> 09:22.140 And again the Nor symbol is just a regulator or gate symbol with a small circle at the output. 09:25.660 --> 09:34.460 Let's also write the symbols of Nand and Nor gates in circuits. 09:35.580 --> 09:36.020 So. 09:38.140 --> 09:40.060 Nor gate basically written like this. 09:40.620 --> 09:45.660 Same as or but small circle here. 09:47.820 --> 09:48.140 Oops. 09:48.180 --> 09:49.140 This was the end. 09:49.660 --> 09:50.060 Yeah. 09:51.420 --> 09:59.100 Nor Nand gate here and small circle at the top. 10:01.980 --> 10:09.660 And let's also write the Nor gate curved opposite C line and. 10:13.460 --> 10:16.180 Circle at the nose. 10:18.620 --> 10:27.700 And here where things get even cooler now there's a pair of logic identities called De Morgan's laws. 10:27.900 --> 10:29.980 And one of them says that. 10:32.340 --> 10:47.220 Note A and b equals note A or so, or symbol note A or not B. 10:48.700 --> 10:50.580 So you can read a lot this. 10:51.620 --> 10:59.580 Not A and B is the same as not A or not B. 11:00.340 --> 11:08.940 This tells us that you can redraw a Nand gate using an Or gate with inverted inputs. 11:09.900 --> 11:12.660 So let's look at it step by step. 11:15.180 --> 11:18.660 We will draw a new diagram here. 11:20.940 --> 11:24.860 This a b not a not b. 11:25.580 --> 11:34.460 Not not a or not b and not a. 11:37.820 --> 11:39.700 Not a and not b. 11:39.740 --> 11:40.140 Yeah. 11:41.100 --> 11:44.620 Here we will have a and b. 11:45.380 --> 11:51.140 So a is going to be equal to 0001. 11:51.140 --> 11:57.740 111011. 11:58.420 --> 12:01.060 So let's get calculating. 12:02.300 --> 12:06.100 So here we will have. 12:08.700 --> 12:21.060 Node A node a node b node a and not b. 12:22.940 --> 12:23.860 And also. 12:26.340 --> 12:29.740 Now note let's first write node a. 12:32.020 --> 12:36.780 Or not b not p. 12:37.340 --> 12:38.820 And here not. 12:41.420 --> 12:44.740 A and b. 12:45.420 --> 12:47.300 Yeah that's basically it. 12:49.420 --> 12:54.730 So here Uh, not a is going to be one again. 12:54.930 --> 13:06.570 One not A00 and not B is going to be one zero. 13:08.690 --> 13:14.330 One zero not A. 13:16.890 --> 13:31.730 Or not B will equal to not a not b one, one, one and zero. 13:35.810 --> 13:36.770 Not a. 13:40.410 --> 13:42.170 Or b. 13:45.090 --> 13:49.370 111 and zero. 13:49.970 --> 13:51.610 Now look at that. 13:51.650 --> 13:52.090 Here. 13:52.730 --> 13:54.010 These are the same. 13:55.530 --> 13:56.490 These are the same. 13:56.690 --> 13:57.610 The Morgan's law. 13:57.730 --> 13:58.170 So. 13:58.330 --> 13:59.050 And look at that. 13:59.050 --> 14:04.370 The output matches the Nand and the truth table perfectly. 14:05.770 --> 14:06.010 And. 14:06.050 --> 14:14.170 Yeah, uh, what you should remember from this lecture is Nand is basically not and nor is basically 14:14.170 --> 14:21.010 not or, and small circles in logic diagrams, uh, like this means inversion. 14:22.290 --> 14:23.330 Uh note here. 14:23.650 --> 14:29.250 And the Morgan's law allows us to write Nand and Nor in alternative forms. 14:29.690 --> 14:36.170 Nand and Nor gates are universal gates, meaning you can build any other gate using just Nand and Nor. 14:36.370 --> 14:43.450 And next up in this course, we will prove this universally by building not and, or and XOR gates using 14:43.450 --> 14:45.490 only Nans or only Nors. 14:45.850 --> 14:46.970 Now, thank you for watching. 14:47.010 --> 14:49.690 And I'm Typhoon and I'm meeting you in next lecture.