WEBVTT 00:00.410 --> 00:05.690 Hello, my name is Typhoon, and in this lecture you will get detailed information about converting 00:05.690 --> 00:13.400 the decimal to binary and vice versa, as well as converting the hexadecimal to decimal and vice versa. 00:14.210 --> 00:24.200 In the world of computers, data is represented using binary digits, commonly referred as zeros and 00:24.200 --> 00:25.250 ones. 00:25.490 --> 00:26.330 Right? 00:26.510 --> 00:35.480 So a binary is the fundamental language that computers use to perform calculations and store information. 00:35.510 --> 00:44.330 However, as humans, we are more accustomed to working with decimal numbers, in this case decimal 00:44.360 --> 00:45.110 here. 00:47.140 --> 00:51.460 Decimal means base ten. 00:52.750 --> 00:53.890 Actually, let's make, uh. 00:53.890 --> 00:56.110 Let's use a different color for this here. 00:56.230 --> 00:57.040 So. 00:58.020 --> 00:58.830 Base. 01:02.140 --> 01:05.410 And hexadecimal means. 01:13.520 --> 01:15.380 Hexadecimal. 01:19.700 --> 01:23.750 Means we call the decimal base. 01:25.760 --> 01:26.270 Gazette. 01:26.270 --> 01:27.240 Gazette Yes. 01:27.260 --> 01:29.670 Page 16. 01:29.750 --> 01:39.230 So here, therefore, understanding the conversion between these different numbers, for example, turning 01:39.230 --> 01:50.390 the decimal to turning the base ten to base 16 or vice versa, turning the converting the base 16 to 01:50.420 --> 01:53.590 base ten is important in computing. 01:53.600 --> 02:00.860 And here in this lecture we will explore in detail how to convert decimal to binary and vice versa. 02:00.860 --> 02:09.800 And you will also learn how to convert the hexadecimal to decimal like this here. 02:09.800 --> 02:11.210 So and vice versa. 02:11.390 --> 02:12.770 So here we will. 02:12.770 --> 02:14.870 Firstly, we will firstly. 02:16.010 --> 02:18.080 And we also have the binary here. 02:18.770 --> 02:20.150 A binary. 02:22.670 --> 02:25.610 And this here we tell this binary only. 02:30.000 --> 02:32.190 Once and. 02:32.960 --> 02:37.310 Zeros or zeros and ones so false or. 02:38.590 --> 02:41.380 Oh, and here, actually, let's. 02:45.980 --> 02:48.080 At this brush here. 02:49.530 --> 02:50.110 The light. 02:50.110 --> 02:50.820 This. 02:51.820 --> 02:53.920 As we will write things on the screen. 02:55.300 --> 02:55.780 Okay. 02:55.900 --> 02:57.220 And also we can also. 03:04.550 --> 03:11.540 Okay, so now we will first start with converting the decimal to binary. 03:11.570 --> 03:16.700 Now let's delve deeper into the process of converting decimal numbers to binary. 03:16.700 --> 03:25.880 And the key concept here is understanding the significance of each digits position in the binary representation. 03:25.880 --> 03:26.780 So. 03:27.740 --> 03:35.670 And the as I said, the binary system binary number system follows the base two. 03:35.690 --> 03:40.580 So remember base ten, base 16 and base. 03:41.520 --> 03:42.570 You're right. 03:43.050 --> 03:47.670 Now, we will delete this because I think we understood that already. 03:49.110 --> 03:50.280 Delete that. 03:53.780 --> 03:56.800 Or converting the decimal to binary. 03:56.810 --> 04:06.590 And in this case, so as I said so and this base two system where each position here represents a power 04:06.590 --> 04:07.190 of two. 04:07.490 --> 04:13.370 So starting from the high mass position, also known as the least significant bit. 04:13.400 --> 04:16.040 So the positions are here. 04:19.830 --> 04:28.800 Q power of 0 to 1, two of three and so on. 04:28.800 --> 04:34.230 So with the exponent increasing as we move to the left. 04:34.230 --> 04:36.060 So it works like this, right? 04:36.210 --> 04:37.920 The first here. 04:38.640 --> 04:41.880 So it works a reverse in, in reverse order here. 04:42.450 --> 04:45.090 So let's actually draw it again. 04:47.420 --> 04:47.900 So. 04:51.430 --> 04:58.570 And now what we're going to do is we will begin with the decimal number you want to convert to binary. 04:58.570 --> 05:03.580 In this case, let's actually write our the title here. 05:04.210 --> 05:06.430 Uh, decimal. 05:09.110 --> 05:09.830 To. 05:10.880 --> 05:11.630 Binary. 05:15.860 --> 05:16.760 In this case. 05:16.760 --> 05:17.600 Here we will. 05:17.600 --> 05:23.690 Let's select the number we want to convert is the 30. 05:25.500 --> 05:27.710 Six right here. 05:27.720 --> 05:36.240 So the first step here, the first step, let's actually we will also write the step steps here. 05:36.630 --> 05:38.340 So the first step. 05:39.870 --> 05:44.670 The first step is we'll begin with the decimal number you want to convert to binary. 05:44.700 --> 05:49.100 Here in this case, it's 36 here. 05:49.110 --> 05:52.740 So in this case it's 36. 05:52.740 --> 06:00.780 And the step two is we will divide the number by two and note down the remainder. 06:00.780 --> 06:07.650 So we will 36 divided by two and we don't have any remainder. 06:07.920 --> 06:11.640 So in this case, it is the zero. 06:14.360 --> 06:22.100 And the step three is continuing, dividing the quotient by two until the point becomes zero. 06:22.100 --> 06:22.670 Right. 06:22.700 --> 06:24.140 So in this case. 06:25.550 --> 06:26.330 We will. 06:27.360 --> 06:32.970 Also 36 divided by two. 06:34.820 --> 06:40.280 And in this case, we will not have the 36 anymore because we already divided it. 06:40.280 --> 06:41.870 So we will need. 06:41.870 --> 06:42.200 Actually. 06:42.200 --> 06:44.030 Let me get the pen here. 06:44.180 --> 06:44.900 Uh, the. 06:46.670 --> 06:47.410 Purser. 06:48.290 --> 06:54.910 So in this case, we will have the 36 divided by two. 06:54.920 --> 07:01.070 So we have the number reminder is zero, but we also have the. 07:03.770 --> 07:04.930 You need the color? 07:04.960 --> 07:05.640 Yes. 07:05.640 --> 07:06.360 Perfect. 07:06.390 --> 07:07.560 Now we will. 07:07.650 --> 07:16.020 We have the remainder of zero and we have the 36 divided by two is. 07:21.150 --> 07:22.080 18. 07:24.060 --> 07:29.550 So we will note that down 18 and the remainder zero. 07:29.670 --> 07:35.940 And here now, we will divide our 18. 07:37.700 --> 07:39.230 It you again. 07:39.230 --> 07:41.780 And here we also have zero. 07:41.930 --> 07:51.710 So now we will in the we will we will continue dividing the quotient by two until the quotient becomes 07:51.710 --> 07:52.670 zero as well. 07:53.570 --> 07:54.590 Uh, so. 07:57.250 --> 07:57.700 Here. 07:57.700 --> 08:03.410 We will now 18 and we what we have left here is nine. 08:03.430 --> 08:05.560 So step four again. 08:06.520 --> 08:08.860 And nine two again. 08:08.860 --> 08:12.970 And as you can see here, we have one reminder here. 08:15.290 --> 08:16.550 And our. 08:17.680 --> 08:19.180 Here is for. 08:22.740 --> 08:24.390 And now we will again. 08:24.630 --> 08:26.400 Step five is. 08:31.320 --> 08:33.720 Or divide by two. 08:35.690 --> 08:37.910 Zero and two. 08:38.540 --> 08:39.260 And. 08:40.870 --> 08:44.500 Thanks again for divide by two again. 08:44.530 --> 08:44.890 Oops. 08:45.190 --> 08:48.310 Two divided by two by two. 08:48.340 --> 08:50.110 We don't have any reminders. 08:50.110 --> 08:52.300 And we have one here. 09:02.780 --> 09:08.660 And here this is the last step almost for calculating our binaries. 09:08.660 --> 09:14.340 So now we need to divide one by two. 09:14.360 --> 09:14.810 Right. 09:14.810 --> 09:18.970 So step seven, divide one by two. 09:18.980 --> 09:21.410 In this case, we will have zero. 09:21.410 --> 09:26.390 But we left with one reminder. 09:26.390 --> 09:26.750 Right? 09:26.750 --> 09:29.690 So and this is our step. 09:29.690 --> 09:37.220 So let's actually so we actually in this case, in the as a result, we don't need this numbers anymore. 09:37.520 --> 09:42.500 So this is our result which now oops actually. 09:42.530 --> 09:48.920 So our result is starting from top 001001. 09:49.130 --> 09:59.660 And here this the the last step here we will need to write down all the reminders in reverse order and 09:59.660 --> 10:07.710 that will be the binary representation of our decimal number in this case is we will need to. 10:08.670 --> 10:13.680 Right down from the from the. 10:15.930 --> 10:17.120 From the bottom. 10:17.130 --> 10:24.840 So here what we're going to do is so our result is actually let's get the span here again. 10:24.840 --> 10:28.620 Let's color actually let's change the color here. 10:33.420 --> 10:36.510 Okay, so here, this is our result. 10:36.540 --> 10:41.520 So when we turn 36 to binary, we will get this here. 10:42.970 --> 10:43.660 One. 10:44.500 --> 10:45.100 Zero. 10:45.610 --> 10:46.450 Zero. 10:47.220 --> 10:52.110 And here 100 from the bottom. 10:52.200 --> 10:57.090 So reverse order and again, 100. 10:57.540 --> 10:59.850 So 100. 10:59.850 --> 11:02.880 So this is the decimal representation. 11:03.150 --> 11:10.470 So this is the binary representation of our 36 decimal number awaiting you in the next lecture.