0:00:17.450,0:00:21.614 Hello and welcome to the first[br]video of the binary numbers. In 0:00:21.614,0:00:25.431 this video. I would like to[br]introduce you to the binary 0:00:25.431,0:00:29.248 numbers and the binary number[br]system, but for us to understand 0:00:29.248,0:00:34.106 that we need to look at what the[br]decimal number system is and we 0:00:34.106,0:00:38.270 need to look at the powers[br]because powers are at the heart 0:00:38.270,0:00:41.740 of every number systems. So[br]let's start with the powers. 0:00:43.800,0:00:47.680 3 to the power of two is 3 0:00:47.680,0:00:54.721 * 3. And for example, 5[br]to the power of four is 5 0:00:54.721,0:01:00.733 * 5 * 5 * 5. So[br]there are two important concepts 0:01:00.733,0:01:02.737 in here, the power. 0:01:03.760,0:01:07.709 And the base, they both can be[br]any different whole numbers. 0:01:08.640,0:01:14.646 So the power tells us how many[br]times we need to multiply the 0:01:14.646,0:01:19.266 base together. So in this[br]particular case, four tasmac 2 0:01:19.266,0:01:24.810 multiplied the base 5 by itself[br]four times, and in the example 0:01:24.810,0:01:30.354 of three, the two tags need to[br]multiply the three by itself 0:01:30.354,0:01:35.436 twice. Now there are two[br]important powers that we need to 0:01:35.436,0:01:38.208 draw your attention to the first 0:01:38.208,0:01:44.300 one. Is any number to the zero[br]power is by definition is always 0:01:44.300,0:01:46.590 one. For example. 0:01:48.440,0:01:55.992 7 to the power of 0 is 1[br]two to the power of 0 is one 0:01:55.992,0:02:01.656 and 10 to the power of 0 is[br]also one another important 0:02:01.656,0:02:09.208 power. Is any number raised[br]to the first power is just the 0:02:09.208,0:02:11.480 number itself for example? 0:02:13.030,0:02:19.652 7 to the first power equals to[br]7, two to the first power equals 0:02:19.652,0:02:25.328 to two and 10 to the first power[br]is equal to 10. 0:02:27.160,0:02:29.160 By definition, the decimal 0:02:29.160,0:02:35.860 number system. Is a[br]base 10 positional. 0:02:37.970,0:02:39.040 Number system. 0:02:41.170,0:02:43.730 Which uses 10 digits. 0:02:46.130,0:02:52.850 And these 10 digits are 012 all[br]the way up to 9. So that's the 9 0:02:52.850,0:02:54.950 digits plus zero, which makes 0:02:54.950,0:03:01.631 them 10. Now what does it mean[br]based on and positional the base 0:03:01.631,0:03:07.163 10 taskview that using 10 digits[br]and every place value or every 0:03:07.163,0:03:11.773 position is represented by[br]powers of 10 and it's a 0:03:11.773,0:03:16.383 positional number system because[br]if you place digits at different 0:03:16.383,0:03:19.610 positions they represent[br]different values. The former 0:03:19.610,0:03:24.681 mathematics is representing each[br]of the place values tend to zero 0:03:24.681,0:03:26.525 10 to the one. 0:03:27.610,0:03:34.596 1:50 2:50 and so[br]on now what they mean as 0:03:34.596,0:03:41.668 numbers? 10 to 0 as we said[br]before, it's 110 to the one 0:03:41.668,0:03:47.108 Eastern tented it too, is 100[br]and 2:50 is 1000. 0:03:48.660,0:03:53.440 It might seems a little bit[br]overcomplicated when you think 0:03:53.440,0:03:59.176 about the decimal numbers, but[br]it is already built into the way 0:03:59.176,0:04:04.912 that we read our numbers. For[br]example, if you read out 573 0:04:04.912,0:04:10.648 just the way you say the number[br]you talk about decimal place 0:04:10.648,0:04:16.862 values 573, so the hundred 500[br]tells you that five is at the 0:04:16.862,0:04:22.617 hundreds place. The 70 tells you[br]that 70s at the 10s place and 0:04:22.617,0:04:27.501 three tells you that three is at[br]the units place. Now, what 0:04:27.501,0:04:32.385 happens if I use the same 3[br]digits but in a slightly 0:04:32.385,0:04:36.048 different order? So what happens[br]if I say 735? 0:04:37.130,0:04:39.041 Well, as I was reading out the 0:04:39.041,0:04:44.690 number. You probably notice that[br]now is 7 at the hundreds place, 0:04:44.690,0:04:50.710 three is at the 10 space and[br]five is at the units place. So 0:04:50.710,0:04:55.010 depending on which place value[br]and placing or which position 0:04:55.010,0:04:58.880 and placing the digits, they[br]will represent different values. 0:04:58.880,0:05:04.900 The five in the first number is[br]105 in the second number is just 0:05:04.900,0:05:10.490 five units. The three in the[br]first number is 3 units, but in 0:05:10.490,0:05:11.780 the second number. 0:05:11.940,0:05:16.087 E 310 switches 30 and the[br]seven in the first number 0:05:16.087,0:05:20.234 is seven 10s, which is 70[br]and in the second number 0:05:20.234,0:05:22.119 is 700 which is 700. 0:05:23.540,0:05:28.428 Now I would like to draw your[br]attention to the rule of the 0:05:28.428,0:05:33.316 zeros because so far I just[br]picked out any digits which is a 0:05:33.316,0:05:38.580 non 0 digit. But what happens if[br]I have good zeros in my number? 0:05:38.580,0:05:41.212 For example? What's the[br]difference between 1007? 0:05:42.380,0:05:48.661 Andseventeen well without having[br]the zeros in the number I end 0:05:48.661,0:05:54.942 up with a very much smaller[br]number, so the zeros are 0:05:54.942,0:05:57.226 so-called place value holders. 0:05:58.600,0:06:04.242 So today telling me that at this[br]place value I'm not using any of 0:06:04.242,0:06:09.481 the place value by placing the[br]zero. So in this case I'm using 0:06:09.481,0:06:15.123 seven of the units, not using[br]any of the 10s an I'm not using 0:06:15.123,0:06:19.556 any of the hundreds and I'm[br]using one of the thousands 0:06:19.556,0:06:24.392 without the zeros here. I'm just[br]telling you that I'm using seven 0:06:24.392,0:06:27.616 or the ones and I'm using one of 0:06:27.616,0:06:31.630 the tents. You will agree with[br]me that the two numbers are 0:06:31.630,0:06:35.712 very, very different, so every[br]time I need to build up a bigger 0:06:35.712,0:06:38.852 number without using the in[br]between place values, I always 0:06:38.852,0:06:40.736 had to place a 0 here. 0:06:45.450,0:06:50.169 Now we can build up a decimal[br]place value table and the former 0:06:50.169,0:06:53.799 place value table would look[br]like this. It's just basically 0:06:53.799,0:06:57.429 the heading you have got the[br]powers and the equivalent 0:06:57.429,0:07:01.785 decimal values. Now how can you[br]use a place value table like 0:07:01.785,0:07:05.415 this to position different[br]numbers in that? Now we talked 0:07:05.415,0:07:09.771 about a few different numbers,[br]so let's see what they look like 0:07:09.771,0:07:12.312 in the place where you table so. 0:07:12.840,0:07:18.948 573 you put a five in the[br]hundreds, seven in the Times 0:07:18.948,0:07:25.565 Seven in the 10s, and three in[br]the units column. If we talking 0:07:25.565,0:07:29.128 about 735, we mix up the order. 0:07:29.860,0:07:36.328 Of the digits 17. One of the[br]10s. Seven of the units and 1007 0:07:36.328,0:07:42.334 one of the thousand. None of the[br]hundreds. None of the 10s and 0:07:42.334,0:07:44.182 seven over the units. 0:07:44.950,0:07:50.494 One thing I'd like you to notice[br]is when you look at the place 0:07:50.494,0:07:55.246 value table. If you're going[br]from right to left, you can spot 0:07:55.246,0:07:59.998 that the numbers from place[br]value to place while you get 10 0:07:59.998,0:08:03.958 times bigger, so the values[br]themselves, the place where used 0:08:03.958,0:08:05.542 gets 10 times bigger. 0:08:06.410,0:08:11.786 Now if we reverse the order and[br]we going from left to right, the 0:08:11.786,0:08:16.010 place values themselves get 10[br]times smaller, so this is again 0:08:16.010,0:08:19.466 another important feature of the[br]place values themselves, which 0:08:19.466,0:08:24.842 will help us to extend the place[br]value table in a later video to 0:08:24.842,0:08:25.994 introduce smaller numbers. 0:08:27.970,0:08:31.640 Now we have got all the[br]conceptual understanding that we 0:08:31.640,0:08:35.677 need to build up the binary[br]numbers. Binary numbers are very 0:08:35.677,0:08:38.613 important for computer science[br]because binary numbers are 0:08:38.613,0:08:42.283 basically the way to communicate[br]to the computer. Remember that 0:08:42.283,0:08:46.320 the computer at a very basic[br]level will type up small 0:08:46.320,0:08:49.623 electrical circuits, and you can[br]either turn on electrical 0:08:49.623,0:08:53.660 circuits on or off, and in the[br]different combinations of these 0:08:53.660,0:08:57.330 electric circuits you can tell[br]the computer to do different 0:08:57.330,0:09:01.126 instructions. So depending on[br]what kind of binary number 0:09:01.126,0:09:04.519 instructions you're giving to[br]the computer, the computer will 0:09:04.519,0:09:07.158 carry out different calculations[br]or different instructions. 0:09:07.940,0:09:14.916 By definition, the binary[br]number system is base 0:09:14.916,0:09:18.404 two positional number system. 0:09:19.420,0:09:22.188 We using 2 digits. 0:09:23.980,0:09:26.996 And these two digits are[br]zero and one. 0:09:28.490,0:09:33.458 So what does the place where you[br]table look for the binary 0:09:33.458,0:09:38.012 numbers? But because it's a base[br]two number system, every place 0:09:38.012,0:09:42.566 value is a power of two. So what[br]are these powers? 0:09:43.220,0:09:49.646 2 to the power of 0 two to the[br]power of 1 two to the power of 2 0:09:49.646,0:09:55.358 to the power of. 3 two to the[br]power of four. 2 to the power of 0:09:55.358,0:09:59.999 5 and I can go on forever. As[br]you see the differences now. 0:10:00.330,0:10:04.246 That instead of base 10, I'm[br]just replacing the Terminator 2, 0:10:04.246,0:10:08.518 but the powers themselves stay[br]the same. Now what does it mean 0:10:08.518,0:10:13.146 for the actual values? What is 2[br]to the zero? While remember any 0:10:13.146,0:10:18.130 number to the Zero power is 1[br]two to the one, any number to 0:10:18.130,0:10:24.182 the first power itself, so it's[br]2 two to two 2 * 2 is 4, two to 0:10:24.182,0:10:30.234 three 2 * 2 * 2 is 8, two to[br]four is 16 and two to five. 0:10:30.340,0:10:33.790 He's 32 and I can go[br]on for higher values. 0:10:35.080,0:10:38.952 So when we look at the place[br]values themselves compared to 0:10:38.952,0:10:43.528 the decimals, Now when I go from[br]right to left, the place values 0:10:43.528,0:10:49.160 get doubled. So from one we can[br]get to 2 from 2 began get to 4 0:10:49.160,0:10:54.792 from 4 we can get to 8, they[br]double up and if I go from left 0:10:54.792,0:10:59.368 to right the opposite direction[br]they get halved from 32 to 16 I 0:10:59.368,0:11:05.000 get by having it and from 16 to[br]8 I get by having it again so. 0:11:05.060,0:11:09.416 This is a common feature of the[br]place where you tables any 0:11:09.416,0:11:12.683 number system because there are[br]other different number systems. 0:11:12.683,0:11:17.039 Every time when you go from[br]right to left, the place values 0:11:17.039,0:11:18.854 get multiplied by the base. 0:11:20.690,0:11:24.218 And when you go from left to[br]right, the place values get 0:11:24.218,0:11:25.394 divided by the base. 0:11:28.150,0:11:32.258 So when we look at the binary[br]place value table, it's like the 0:11:32.258,0:11:35.734 numbers I showed you before, but[br]put into a nicer format. 0:11:36.980,0:11:40.736 So what happens in the here in[br]the decimal place value table? 0:11:40.736,0:11:44.805 We had quite a lot of different[br]digits that we could play around 0:11:44.805,0:11:48.874 with. We had the digits from[br]zero to 9, but what happens in 0:11:48.874,0:11:52.943 binary? Which 2 digits can we[br]use here? Just the zero and one. 0:11:53.580,0:11:58.024 So. A binary number is[br]nothing else but a string 0:11:58.024,0:11:59.408 of ones and zeros. 0:12:01.060,0:12:05.656 For example, this is a binary[br]number. What it means then for 0:12:05.656,0:12:10.252 the place values is that with[br]one I'm saying that use the 0:12:10.252,0:12:14.082 corresponding place value and[br]with zero I'm saying don't use 0:12:14.082,0:12:17.529 the corresponding place value,[br]so the placeholder property of 0:12:17.529,0:12:21.359 the zero becomes really[br]important and comes up a lot 0:12:21.359,0:12:23.657 more often than in decimal[br]numbers. 0:12:25.230,0:12:31.574 Let's look at a few more binary[br]numbers. So basically I can just 0:12:31.574,0:12:37.918 use any ones and any zeros and[br]place them in any order whatever 0:12:37.918,0:12:43.774 to build upon binary number. So[br]let's say 1011001 it's a binary 0:12:43.774,0:12:49.142 number, 100001 is also binary[br]number, or 1011. Again a binary 0:12:49.142,0:12:54.510 number. Now you probably notice[br]that because we only using ones 0:12:54.510,0:12:59.610 and zeros. Every single one of[br]them could also be a decimal 0:12:59.610,0:13:04.458 number. For example, the last[br]one could be 1011 in decimal. So 0:13:04.458,0:13:08.498 how can we make a distinction[br]between binary and decimal? 0:13:10.470,0:13:14.170 So there is a very common[br]notation to distinguish between 0:13:14.170,0:13:18.610 binary and decimal numbers. So[br]if you see a number which only 0:13:18.610,0:13:23.420 uses ones and zeros to make sure[br]that this is a binary number, 0:13:23.420,0:13:27.860 you put a little two in[br]subscript. And if you want to 0:13:27.860,0:13:31.930 indicate that this is a decimal[br]number, you put a little 0:13:31.930,0:13:35.630 subscript of 10, indicating that[br]this is a decimal number. 0:13:36.480,0:13:41.676 So if it's not clear enough from[br]context, always look for the 0:13:41.676,0:13:46.439 subscript. It is a binary[br]number. Or is it a decimal 0:13:46.439,0:13:50.769 number? Now it's very, very[br]important that you are making 0:13:50.769,0:13:54.666 difference between the number[br]itself and the notation of 0:13:54.666,0:13:58.563 signaling which system working[br]in this letter notation, the 0:13:58.563,0:14:04.625 number 2 and here the number 10[br]are not part of the number. As 0:14:04.625,0:14:06.790 long as the calculations go. 0:14:07.120,0:14:11.558 This is just a way of telling[br]me or you or anybody ask that 0:14:11.558,0:14:15.679 this is a binary number. Once[br]we are aware of that, this is 0:14:15.679,0:14:18.849 a binary number. This two[br]becomes redundant, so as long 0:14:18.849,0:14:21.702 as the calculations go, you[br]can leave this number. 0:14:22.840,0:14:26.206 So I hope that you have a[br]better understanding of the 0:14:26.206,0:14:29.266 binary and the decimal number[br]systems in the next few 0:14:29.266,0:14:32.938 videos. I will show you what[br]we can do with the binary 0:14:32.938,0:14:33.244 numbers.