1 1 00:00:00,510 --> 00:00:01,940 Now, at this point of the course, 2 2 00:00:01,940 --> 00:00:04,890 we're about to jump into the area that most students dread 3 3 00:00:04,890 --> 00:00:06,160 when it comes to networking. 4 4 00:00:06,160 --> 00:00:08,210 And this is known as subnetting. 5 5 00:00:08,210 --> 00:00:10,340 Now, don't worry, I'm going to get you through it. 6 6 00:00:10,340 --> 00:00:11,340 But this is probably one 7 7 00:00:11,340 --> 00:00:13,550 of the hardest concepts on the exam, 8 8 00:00:13,550 --> 00:00:15,850 you may need to go through this section a couple of times 9 9 00:00:15,850 --> 00:00:17,390 to make sure you grasp it. 10 10 00:00:17,390 --> 00:00:19,500 Now, what we're going to do is I'm going to go through 11 11 00:00:19,500 --> 00:00:21,590 and we're going to do the hard way first, 12 12 00:00:21,590 --> 00:00:24,180 so you understand the theory and how it all works. 13 13 00:00:24,180 --> 00:00:26,310 Then, I'm going to show you a shortcut 14 14 00:00:26,310 --> 00:00:28,780 and how to get through it for the exam a lot easier. 15 15 00:00:28,780 --> 00:00:31,250 But please don't skip the next couple of lessons 16 16 00:00:31,250 --> 00:00:32,830 of going through the hard way first, 17 17 00:00:32,830 --> 00:00:34,550 because if you don't understand the hard way, 18 18 00:00:34,550 --> 00:00:36,980 the easy way will make zero sense to you. 19 19 00:00:36,980 --> 00:00:40,070 So, as we go forward, we're going to stop and take this lesson 20 20 00:00:40,070 --> 00:00:42,470 to talk about computer mathematics. 21 21 00:00:42,470 --> 00:00:45,060 Now, this is important because computers do their numbering 22 22 00:00:45,060 --> 00:00:47,720 and do math a little bit differently than we do. 23 23 00:00:47,720 --> 00:00:51,180 Now, as a kid, you learn to count in what's known as Base-10. 24 24 00:00:51,180 --> 00:00:52,910 This is a decimal number, right? 25 25 00:00:52,910 --> 00:00:54,200 Decimal meaning 10. 26 26 00:00:54,200 --> 00:00:56,787 And so, when I count, you would start at zero, 27 27 00:00:56,787 --> 00:00:59,810 and it goes zero, one, two, three, four, five, six , seven, 28 28 00:00:59,810 --> 00:01:00,980 eight, nine. 29 29 00:01:00,980 --> 00:01:02,660 Now, what comes next? 30 30 00:01:02,660 --> 00:01:04,940 Well, we go to the second column, we put a one there, 31 31 00:01:04,940 --> 00:01:05,850 and we go back to zero. 32 32 00:01:05,850 --> 00:01:08,420 So, now we go from nine to 10. 33 33 00:01:08,420 --> 00:01:09,460 And then, we keep counting up, 34 34 00:01:09,460 --> 00:01:11,680 and eventually, we get to 98, 99. 35 35 00:01:11,680 --> 00:01:13,680 And then go, "Oh, I need another column," 36 36 00:01:13,680 --> 00:01:15,670 put another one there and add two zeros. 37 37 00:01:15,670 --> 00:01:16,760 That's 100. 38 38 00:01:16,760 --> 00:01:18,960 So I go 98, 99, 100, right? 39 39 00:01:18,960 --> 00:01:20,250 And that's the whole idea here 40 40 00:01:20,250 --> 00:01:22,220 when we talk about decimal, right? 41 41 00:01:22,220 --> 00:01:23,110 When we talk about decimal, 42 42 00:01:23,110 --> 00:01:25,330 we only have 10 choices for the numbers. 43 43 00:01:25,330 --> 00:01:28,750 Each decimal place can only be zero, one, two, three, four, 44 44 00:01:28,750 --> 00:01:30,110 five, six, seven, eight, nine. 45 45 00:01:30,110 --> 00:01:31,740 Those are 10 options. 46 46 00:01:31,740 --> 00:01:32,900 Now, computers and networks 47 47 00:01:32,900 --> 00:01:35,150 don't actually understand decimal natively. 48 48 00:01:35,150 --> 00:01:36,640 So, even though we've been using decimal 49 49 00:01:36,640 --> 00:01:38,550 when talking about IPv4 addresses, 50 50 00:01:38,550 --> 00:01:40,510 that's not how computers see them. 51 51 00:01:40,510 --> 00:01:42,390 Computers do everything in binary, 52 52 00:01:42,390 --> 00:01:44,070 which is base-2 numbering. 53 53 00:01:44,070 --> 00:01:47,040 That means, every single digit is either a one 54 54 00:01:47,040 --> 00:01:50,390 or it's a zero, that's an on or it's an off. 55 55 00:01:50,390 --> 00:01:52,550 That is how computers understand things. 56 56 00:01:52,550 --> 00:01:55,303 And so, when they count, they go 011011100111 57 57 00:01:59,510 --> 00:02:01,310 and they keep going like that. 58 58 00:02:01,310 --> 00:02:03,930 The one zero is actually the number two for us. 59 59 00:02:03,930 --> 00:02:08,210 But for them in binary, that is actually a one zero 60 60 00:02:08,210 --> 00:02:11,010 and one zero equates to two, because it's the third thing, 61 61 00:02:11,010 --> 00:02:13,300 we got to zero one two. 62 62 00:02:13,300 --> 00:02:15,230 Now, that's the way this works with a computer. 63 63 00:02:15,230 --> 00:02:16,860 And so, we have to understand 64 64 00:02:16,860 --> 00:02:18,540 how things are written in decimal 65 65 00:02:18,540 --> 00:02:20,010 and how things are written in binary, 66 66 00:02:20,010 --> 00:02:22,190 and how to convert between the two. 67 67 00:02:22,190 --> 00:02:23,180 And that's what we're going to talk 68 68 00:02:23,180 --> 00:02:25,250 about in this particular lesson. 69 69 00:02:25,250 --> 00:02:27,860 Now, when we convert from binary to decimal, 70 70 00:02:27,860 --> 00:02:29,540 we're going to do this using a table 71 71 00:02:29,540 --> 00:02:31,150 that I have here on the screen. 72 72 00:02:31,150 --> 00:02:33,310 Each number is a factor of two. 73 73 00:02:33,310 --> 00:02:35,270 And so, this way, we can start going 74 74 00:02:35,270 --> 00:02:37,170 and putting them as placeholders of one 75 75 00:02:37,170 --> 00:02:39,520 or zero as we go through each place. 76 76 00:02:39,520 --> 00:02:43,410 So, if we start on the right, and we go left, we have one, 77 77 00:02:43,410 --> 00:02:46,230 and then, we have a place of one, right? 78 78 00:02:46,230 --> 00:02:49,840 Now, if I put a one zero in the second and first columns, 79 79 00:02:49,840 --> 00:02:51,910 this is going to become two. 80 80 00:02:51,910 --> 00:02:54,350 And we keep going through as we keep counting. 81 81 00:02:54,350 --> 00:02:55,870 Now, if you're not getting it quite yet, 82 82 00:02:55,870 --> 00:02:57,830 you will by the end of this lesson, I promise. 83 83 00:02:57,830 --> 00:02:59,050 So, let's just keep going ahead 84 84 00:02:59,050 --> 00:03:01,130 and we're going to do some examples together. 85 85 00:03:01,130 --> 00:03:03,973 Let's say I give you the binary number of 10010110. 86 86 00:03:06,450 --> 00:03:07,700 And I asked you to tell me 87 87 00:03:07,700 --> 00:03:10,420 what is this if I put it into decimal? 88 88 00:03:10,420 --> 00:03:12,680 Well, we're going to first by populating the table 89 89 00:03:12,680 --> 00:03:15,160 starting from the right and going to the left. 90 90 00:03:15,160 --> 00:03:16,930 And so, we're going to put the number there 91 91 00:03:16,930 --> 00:03:18,120 that we have from right to left 92 92 00:03:18,120 --> 00:03:20,150 and end up with what you see here on the screen, 93 93 00:03:20,150 --> 00:03:24,650 it turns into 1001011, and zero. 94 94 00:03:24,650 --> 00:03:26,630 Now, there's a place where there's a one, 95 95 00:03:26,630 --> 00:03:28,360 and I'm going to add the number above it. 96 96 00:03:28,360 --> 00:03:33,360 So, if I see something like 128, plus 16, plus four plus two, 97 97 00:03:34,400 --> 00:03:38,120 and I add that all together, I'm going to get 150. 98 98 00:03:38,120 --> 00:03:43,120 That is the number 10010110 in binary, 99 99 00:03:43,270 --> 00:03:46,020 and it translates to 150 in decimal. 100 100 00:03:46,020 --> 00:03:48,480 You see how easy that is if you have the little chart. 101 101 00:03:48,480 --> 00:03:50,370 So, if you make this chart on your paper, 102 102 00:03:50,370 --> 00:03:51,510 when you sit down for the exam, 103 103 00:03:51,510 --> 00:03:53,920 it's going to make things a lot easier for you. 104 104 00:03:53,920 --> 00:03:55,970 Again, going from right to left on the chart, 105 105 00:03:55,970 --> 00:04:00,540 each position starts out with the number of one, two 106 106 00:04:00,540 --> 00:04:04,410 four, eight, 16, 32, 64, 128, 107 107 00:04:04,410 --> 00:04:07,530 we keep multiplying by two as we go from right to left. 108 108 00:04:07,530 --> 00:04:09,200 And so, if I added up every single one 109 109 00:04:09,200 --> 00:04:10,400 of those with one in it, 110 110 00:04:10,400 --> 00:04:13,760 guess what the biggest number I could get is? 255. 111 111 00:04:13,760 --> 00:04:16,420 Which, if you remember when I talked about IPv4, 112 112 00:04:16,420 --> 00:04:20,470 all my numbers were either zero all the way up through 255. 113 113 00:04:20,470 --> 00:04:21,970 That's my four octets. 114 114 00:04:21,970 --> 00:04:23,920 Well, that's because I have eight digits 115 115 00:04:23,920 --> 00:04:25,840 in each of those octets, right? 116 116 00:04:25,840 --> 00:04:27,800 And each digit, each binary digit, 117 117 00:04:27,800 --> 00:04:29,700 can only hold a one or a zero. 118 118 00:04:29,700 --> 00:04:31,560 Now, what if I gave you a decimal number, 119 119 00:04:31,560 --> 00:04:32,880 like from an IP address 120 120 00:04:32,880 --> 00:04:34,670 and asked you to convert that to binary? 121 121 00:04:34,670 --> 00:04:35,810 Could you do it? 122 122 00:04:35,810 --> 00:04:36,770 Well, the answer is yes, 123 123 00:04:36,770 --> 00:04:39,450 it's the exact same process we just did. 124 124 00:04:39,450 --> 00:04:41,630 So, let's take a number from 167 125 125 00:04:41,630 --> 00:04:43,800 and convert it backwards to binary. 126 126 00:04:43,800 --> 00:04:45,960 That'd be one of the octets inside of an IP address, 127 127 00:04:45,960 --> 00:04:46,930 for instance. 128 128 00:04:46,930 --> 00:04:48,300 Well, instead of adding up, 129 129 00:04:48,300 --> 00:04:49,820 we're going to to be subtracting. 130 130 00:04:49,820 --> 00:04:51,890 So, when I do this, I'll take 167 131 131 00:04:51,890 --> 00:04:53,460 and I'll start from the left. 132 132 00:04:53,460 --> 00:04:56,300 Can I take 128 out of 167? 133 133 00:04:56,300 --> 00:04:57,220 Yes, I can. 134 134 00:04:57,220 --> 00:04:59,000 And I'll have 39 leftover. 135 135 00:04:59,000 --> 00:05:00,440 Then, I go to the next column. 136 136 00:05:00,440 --> 00:05:01,560 That's 64. 137 137 00:05:01,560 --> 00:05:03,760 Can I take 64 from 39? 138 138 00:05:03,760 --> 00:05:05,550 No, because there's not enough there. 139 139 00:05:05,550 --> 00:05:08,010 So, I'll put a zero under the 64 column. 140 140 00:05:08,010 --> 00:05:10,480 Then, I'll say, Can I take 32 out of 39? 141 141 00:05:10,480 --> 00:05:11,400 Yes, I can. 142 142 00:05:11,400 --> 00:05:12,930 And I'll have seven left over. 143 143 00:05:12,930 --> 00:05:14,590 So, I'll put one in that column. 144 144 00:05:14,590 --> 00:05:16,670 Then. I look, can I take 16 from seven? 145 145 00:05:16,670 --> 00:05:18,340 No, so I put a zero. 146 146 00:05:18,340 --> 00:05:19,620 How about eight from seven? 147 147 00:05:19,620 --> 00:05:21,290 No, so I put a zero. 148 148 00:05:21,290 --> 00:05:22,640 How about four from seven? 149 149 00:05:22,640 --> 00:05:24,650 Yes, and that leaves me with three. 150 150 00:05:24,650 --> 00:05:26,540 Can I go ahead and take two from three? 151 151 00:05:26,540 --> 00:05:28,600 Yes, I'll put a one in that column. 152 152 00:05:28,600 --> 00:05:30,100 And then, can I take one from one? 153 153 00:05:30,100 --> 00:05:32,230 Yes, and I'll put a one down for that. 154 154 00:05:32,230 --> 00:05:34,970 And this is how you convert from decimal back to binary, 155 155 00:05:34,970 --> 00:05:36,890 you're going to subtract all the way down. 156 156 00:05:36,890 --> 00:05:39,080 Just like what I went from binary to decimal, 157 157 00:05:39,080 --> 00:05:41,230 I ended up going from decimal to binary, 158 158 00:05:41,230 --> 00:05:43,010 I'm going to go ahead and subtract. 159 159 00:05:43,010 --> 00:05:45,410 Now, either way, if you have this chart down, 160 160 00:05:45,410 --> 00:05:46,490 these factors of two, 161 161 00:05:46,490 --> 00:05:48,910 it makes these problems very, very easy. 162 162 00:05:48,910 --> 00:05:50,750 So, now that we have that example underway, 163 163 00:05:50,750 --> 00:05:53,743 and we see that 167 is actually 10100111. 164 164 00:05:56,060 --> 00:05:58,660 How can I check my math and make sure I got it right? 165 165 00:05:58,660 --> 00:06:00,570 Well, I can go the other way. 166 166 00:06:00,570 --> 00:06:03,610 And I can add up the numbers and they all come back to 167. 167 167 00:06:03,610 --> 00:06:05,270 That means, I did the problem correctly. 168 168 00:06:05,270 --> 00:06:06,830 So, let's check our answer, 169 169 00:06:06,830 --> 00:06:11,830 128 plus 32 plus four plus two plus one, that equals 167. 170 170 00:06:12,180 --> 00:06:14,540 That means, we did our math problem correctly. 171 171 00:06:14,540 --> 00:06:16,930 Now, in the next lesson, I'm going to give you some problems. 172 172 00:06:16,930 --> 00:06:18,410 And we're going to try these together 173 173 00:06:18,410 --> 00:06:20,070 and see if you understand these concepts 174 174 00:06:20,070 --> 00:06:21,940 because it is really, really important 175 175 00:06:21,940 --> 00:06:23,223 as we go into subnetting.