WEBVTT 00:00:00.000 --> 00:00:03.700 Welcome back to CSE 316 — Data Communication and Networking. 00:00:03.750 --> 00:00:12.700 This is the detailed video version of Session fifteen, and it is the session the last four have been building towards. 00:00:13.070 --> 00:00:20.520 One line — eleven dot ten dot three dot ten slash twenty-two — and six customers, arriving in two waves. 00:00:20.570 --> 00:00:28.130 Twelve marks, three parts, and I promise you now: not one idea in it that you do not already own. 00:00:28.180 --> 00:00:35.630 Part (a) is Session eleven. Parts (b) and (c) are Session fourteen, run six times. 00:00:35.680 --> 00:00:44.145 The only genuinely new thing is a clause in the question, and we will spend a section on it. 00:00:44.195 --> 00:00:48.235 This is not "a" question on this course. 00:00:48.285 --> 00:00:57.235 It is the highest-value question of the addressing arc: twelve marks, three parts, and it recurs on the final in this form or a close variant. 00:00:57.665 --> 00:01:06.615 If you can produce this answer cold, on blank paper, in fifteen minutes, you have taken the addressing block of the paper off the table. 00:01:06.685 --> 00:01:15.635 So here is the promise. By the end of this session the complete answer is on the page, audited, and every hard step is derived rather than asserted. 00:01:16.035 --> 00:01:23.735 Not shown to you. Derived — so that when the numbers change, and they will, the method still runs. 00:01:23.785 --> 00:01:31.345 The session is a harvest, not a challenge. Nothing new is taught today, and every step uses a method you already have. 00:01:31.395 --> 00:01:40.345 One thing before we start. Read the whole problem before you write anything — the parent block, then three organisations, then three more, and the clause that says nobody in wave one may move. 00:01:46.624 --> 00:01:49.194 Section one. Dissect the question. 00:01:49.244 --> 00:01:58.194 Every part of this problem is a lecture you have already had. What is being tested is whether your ritual survives pressure. 00:01:59.224 --> 00:02:03.794 Take the question apart before you touch a single number. 00:02:03.844 --> 00:02:12.024 Part (a): first address, last address, and the number of addresses for eleven dot ten dot three dot ten slash twenty-two. 00:02:12.074 --> 00:02:17.814 That is the Session eleven ritual. Two free marks — with a stopwatch. 00:02:17.864 --> 00:02:24.134 Part (b): three organisations wanting thirty, two hundred and fifty, and fifteen addresses. 00:02:24.184 --> 00:02:31.404 Round, sort, align. That is Session fourteen's entire lecture, applied three times. 00:02:31.454 --> 00:02:40.404 Part (c): three more customers — five hundred, a hundred, fifty. This is the part where the alignment rule decides the answer. 00:02:40.834 --> 00:02:47.634 Because of that clause. Read it twice. Wave one is concrete. Wave two must fold itself around it. 00:02:47.684 --> 00:02:56.634 Nothing in the three parts is an idea you do not already own. This question does not test cleverness. 00:02:57.107 --> 00:03:01.567 That clause is the only new pressure in the whole question. 00:03:01.617 --> 00:03:08.977 The first three organisations are live networks. They have routers, printers, servers, and opinions. 00:03:09.027 --> 00:03:17.977 Renumbering a running network means touching every machine on it — so "just shift Org1 along a bit" is not an option available to anyone. 00:03:19.077 --> 00:03:23.597 Which means wave two does not inherit a block. It inherits a shape. 00:03:23.647 --> 00:03:32.167 Whatever wave one left behind — a clean tail, or a scarred middle — is the raw material wave two has to work with. 00:03:32.217 --> 00:03:36.127 And that is why last session's ordering rule stops being a preference. 00:03:36.177 --> 00:03:44.937 With six customers and a fixed parent, wrong order does not merely strand addresses. It can leave a customer with nowhere legal to go at all. 00:03:44.987 --> 00:03:53.937 Note the shape of the difficulty: it is a constraint, not a technique. The technique is unchanged. 00:03:54.703 --> 00:04:01.593 Part (a). Four facts, and the ritual is unchanged from Session eleven. 00:04:01.643 --> 00:04:07.513 N. Thirty-two minus twenty-two is ten, two to the ten is one thousand and twenty-four. 00:04:07.563 --> 00:04:12.643 You should have that before you have finished reading the address. 00:04:12.693 --> 00:04:21.643 Mask. Twenty-two over eight is two, remainder six. Two full octets of two fifty-five, then six ones — which is two fifty-two. 00:04:21.823 --> 00:04:30.773 Two five five, two five five, two five two, zero. One division and one ladder lookup, with no binary written down. 00:04:31.853 --> 00:04:38.963 Now the AND, and the fight is in the third octet. Three in binary is six zeros and then one-one. 00:04:39.013 --> 00:04:46.853 Two fifty-two keeps the top six bits and throws away the bottom two. So three AND two fifty-two is zero. 00:04:46.903 --> 00:04:55.853 First address: eleven dot ten dot zero dot zero. Not eleven dot ten dot three dot zero — and that is the trap on this part. 00:04:56.693 --> 00:05:05.643 Last. One thousand and twenty-four is four runs of two hundred and fifty-six, so the third octet walks zero, one, two, three. 00:05:06.013 --> 00:05:11.413 Last address: eleven dot ten dot three dot two fifty-five. 00:05:11.463 --> 00:05:20.413 And there is the answer row: one thousand and twenty-four, two five five two five five two five two zero, eleven dot ten dot zero dot zero, eleven dot ten dot three dot two fifty-five. 00:05:24.133 --> 00:05:33.083 Two marks, well under a minute, once the ritual is automatic. Ten marks to go — and every one of them is Session fourteen, run once per organisation. 00:05:37.726 --> 00:05:44.586 Part (b). Three organisations, and before you place anything, round and sort. 00:05:44.636 --> 00:05:53.106 Org1 wants thirty. Thirty does not fit in sixteen, so upward to thirty-two. That is a slash twenty-seven. 00:05:53.156 --> 00:06:02.106 Org2 wants two hundred and fifty. Up to two fifty-six — a slash twenty-four, and the largest of the three by a wide margin. 00:06:02.456 --> 00:06:11.406 Org3 wants fifteen. Up to sixteen — a slash twenty-eight. Snug, with one address to spare after the two overheads. 00:06:11.956 --> 00:06:18.556 And here is the move a marker looks for first: the placement order is Org2, then Org1, then Org3. 00:06:18.606 --> 00:06:26.486 The question numbers them one, two, three. That is their numbering. Ours is largest first. 00:06:26.536 --> 00:06:35.486 Largest first is not a preference. You proved it last session, and you are about to re-prove it on this block in about ten minutes. 00:06:37.559 --> 00:06:44.599 Before the first placement, fix the template, because you are about to run it six times. 00:06:44.649 --> 00:06:52.159 One: next free address. Where did the previous block stop? That is where this one starts looking. 00:06:52.209 --> 00:06:58.489 Two: alignment. Offset divided by this block's own size — is it whole? If not, move up to the next multiple. 00:06:58.539 --> 00:07:07.479 Say that division out loud even when the answer is obvious. It is the step people skip, and it is the step the marks live in. 00:07:07.529 --> 00:07:15.079 Three and four: first address, and last address — first plus N minus one. The Session eleven ritual, unchanged. 00:07:15.129 --> 00:07:24.079 Five: the name. First address, slash the new prefix. And write it down — a design without names is a picture, not an answer. 00:07:25.469 --> 00:07:34.419 Six organisations, five sentences each. Thirty sentences, most of them arithmetic you could do while annoyed — and that is the entire twelve-mark answer. 00:07:40.959 --> 00:07:48.259 Forty-two seconds, and the whole question in one bar. Wave one decides wave two's options. 00:07:48.309 --> 00:07:57.259 There is the parent: one thousand and twenty-four addresses, from eleven dot ten dot zero dot zero to eleven dot ten dot three dot two fifty-five. 00:07:58.299 --> 00:08:02.269 Empty, for the last time in this session. 00:08:02.319 --> 00:08:09.809 Wave one, rounded: two fifty-six, thirty-two, sixteen. And re-ordered — Org2, Org1, Org3. 00:08:09.859 --> 00:08:15.099 Their numbering is on the left; ours is the arrow. 00:08:15.149 --> 00:08:24.019 Org2 takes the front door and eats exactly two fifty-six. Org1 lands at two fifty-six, Org3 at two eighty-eight. 00:08:24.069 --> 00:08:33.019 Three tenants, flush, no gaps — and the grey tail is the ISP's remaining stock: seven hundred and twenty addresses. 00:08:33.749 --> 00:08:42.699 Six months later, three more customers. Five hundred, a hundred, fifty — rounding to five twelve, one twenty-eight, sixty-four. 00:08:43.239 --> 00:08:47.639 And the clause: nobody in wave one may move. 00:08:47.689 --> 00:08:56.639 Watch Org4. It does not take the next free address. It jumps to offset five hundred and twelve — eleven dot ten dot two dot zero. 00:08:56.769 --> 00:09:04.039 That is the only legal door it has left, and the next section is nothing but that one move. 00:09:04.089 --> 00:09:13.039 Then the strip fills itself. Org5's slash twenty-five at eleven dot ten dot one dot one twenty-eight, Org6's slash twenty-six at one dot sixty-four. 00:09:13.889 --> 00:09:18.109 Backfilled into the space Org4 stepped over. 00:09:18.159 --> 00:09:25.369 And the audit. One thousand and eight allocated, sixteen unused, one thousand and twenty-four total. 00:09:25.419 --> 00:09:34.369 Six tenants, one hole, and it balances. That is the finished answer — now we derive every step of it. 00:09:35.909 --> 00:09:43.529 Now run the template three times. Five sentences each, and I will say them all. 00:09:43.579 --> 00:09:51.569 Org2 first, because it is largest. Next free is offset zero. Zero over two fifty-six is zero — whole, legal. 00:09:51.619 --> 00:10:00.569 First address eleven dot ten dot zero dot zero. Last is that plus two fifty-five: eleven dot ten dot zero dot two fifty-five. Name: eleven dot ten dot zero dot zero slash twenty-four. 00:10:07.129 --> 00:10:14.659 Org1. Next free is offset two fifty-six. Two fifty-six over thirty-two is eight — whole. 00:10:14.709 --> 00:10:20.919 Eleven dot ten dot one dot zero slash twenty-seven, last address one dot thirty-one. 00:10:20.969 --> 00:10:29.919 And notice why that door was open: the slash twenty-four ate exactly two fifty-six, which is a multiple of everything smaller. 00:10:30.279 --> 00:10:37.259 Org3. Next free is two eighty-eight. Two eighty-eight over sixteen is eighteen — whole. 00:10:37.309 --> 00:10:46.259 Eleven dot ten dot one dot thirty-two slash twenty-eight, last address one dot forty-seven. Three tenants, flush, no gaps. 00:10:48.049 --> 00:10:53.629 Allocated: two fifty-six plus thirty-two plus sixteen is three hundred and four. 00:10:53.679 --> 00:11:02.629 So the ISP still holds eleven dot ten dot one dot forty-eight through eleven dot ten dot three dot two fifty-five — seven hundred and twenty addresses. 00:11:04.629 --> 00:11:13.409 Write that range out. It is the line students skip and examiners do not, and it is worth an actual mark for one sentence about leftovers. 00:11:13.459 --> 00:11:22.409 Part (b) done: four marks banked, and the shape wave two has to live inside is now fixed. 00:11:23.425 --> 00:11:30.385 Checkpoint one. Three questions, and I want them on paper before the answers appear. 00:11:30.435 --> 00:11:38.835 One. Give all four facts for eleven dot ten dot three dot ten slash twenty-two, and name the trap in part (a). 00:11:38.885 --> 00:11:47.615 Two. Round and sort requests of thirty, two hundred and fifty and fifteen, and say which is allocated first. 00:11:47.665 --> 00:11:56.205 Three. After wave one, what exactly does the ISP still hold? Give the range and the count. 00:11:56.255 --> 00:12:05.205 One. N is one thousand and twenty-four; mask two five five, two five five, two five two, zero; first eleven dot ten dot zero dot zero; last eleven dot ten dot three dot two fifty-five. 00:12:09.845 --> 00:12:18.795 The trap is writing eleven dot ten dot three dot zero as the first address — three AND two fifty-two is zero, so that octet is zero. 00:12:21.695 --> 00:12:30.645 Two. Thirty-two, two fifty-six and sixteen — a slash twenty-seven, a slash twenty-four and a slash twenty-eight. Sorted descending: Org2 first, then Org1, then Org3. 00:12:33.215 --> 00:12:42.165 Three. Eleven dot ten dot one dot forty-eight through eleven dot ten dot three dot two fifty-five, which is seven hundred and twenty addresses. Writing that sentence is worth a mark on its own. 00:12:49.886 --> 00:12:52.526 Section two. The counterfactual. 00:12:52.576 --> 00:13:01.526 Last session you were told that smallest-first leaves scars. Here is the invoice — in this block, with these customers, in real addresses. 00:13:04.820 --> 00:13:11.180 Suppose you had done the natural thing and allocated them in the order the question numbers them. 00:13:11.230 --> 00:13:17.910 Org1 takes offset zero. Legal — zero over thirty-two is zero — and completely wrong. 00:13:17.960 --> 00:13:26.040 A thirty-two-address tenant has just taken the front door of a two-hundred-and-fifty-six-address alley. 00:13:26.090 --> 00:13:35.040 Now Org2, which needs a multiple of two fifty-six. The next free address is offset thirty-two, and thirty-two over two fifty-six is not whole. 00:13:35.450 --> 00:13:44.400 Neither is sixty-four, or one twenty-eight. The first legal door is offset two fifty-six, so that is where Org2 is forced to go. 00:13:45.300 --> 00:13:53.160 And offsets thirty-two through two fifty-five drop dead. Two hundred and twenty-four addresses, stranded in the middle of the block, 00:13:53.210 --> 00:14:02.160 unreachable by anything larger than a slash twenty-six — because a slash twenty-six is the biggest thing that fits inside that gap on its own lattice. 00:14:03.970 --> 00:14:11.220 And wave two has not even arrived yet. It is about to need every scrap of contiguous space this block has. 00:14:11.270 --> 00:14:14.420 Request order would already have spent it — on nothing. 00:14:14.470 --> 00:14:23.420 Same customers, same total demand, and two hundred and twenty-four addresses of difference. Order is not tidiness. 00:14:24.720 --> 00:14:31.650 Now price those two hundred and twenty-four addresses, because "stranded" is too soft a word. 00:14:31.700 --> 00:14:40.650 As a clean tail at the end of a block, two hundred and twenty-four contiguous addresses can be cut into a slash twenty-six, a slash twenty-seven and a slash twenty-eight, and sold. 00:14:43.020 --> 00:14:47.160 That is real inventory. Three customers' worth. 00:14:47.210 --> 00:14:56.160 As a hole between two tenants, they are mostly dead. Offsets thirty-two to two fifty-five can only house blocks that are aligned inside that gap, 00:14:56.450 --> 00:15:05.400 and the largest of those is a slash twenty-six at offset sixty-four. Everything bigger is refused, however much space the count says you have. 00:15:06.900 --> 00:15:15.310 And nobody can be asked to move. That is the clause in part (c), and it is what makes this mistake permanent rather than embarrassing. 00:15:15.360 --> 00:15:24.310 In this problem the sort is not worth style marks. It is the difference between wave two fitting and wave two failing. 00:15:25.720 --> 00:15:31.580 Back to the correct design, and part (c). Three more customers. 00:15:31.630 --> 00:15:40.580 Org4 wants five hundred. Rounds to five hundred and twelve — a slash twenty-three. This is the block that decides the question. 00:15:40.650 --> 00:15:49.600 Org5 wants a hundred, rounding to one twenty-eight — a slash twenty-five. Org6 wants fifty, rounding to sixty-four — a slash twenty-six. 00:15:50.890 --> 00:15:56.650 Both comfortable sizes, and both easy to place once Org4 has chosen. 00:15:56.700 --> 00:16:00.050 Count the free space before promising any of it. 00:16:00.100 --> 00:16:09.050 Free: eleven dot ten dot one dot forty-eight to the end — seven hundred and twenty addresses. Demanded: five twelve plus one twenty-eight plus sixty-four, which is seven hundred and four. 00:16:13.700 --> 00:16:16.750 Sixteen addresses of slack. Sixteen. 00:16:16.800 --> 00:16:22.750 If even one block starts one notch off its lattice, something in wave two becomes homeless. 00:16:22.800 --> 00:16:31.750 That margin is the whole tension of part (c), and it is why the ordering rule stops being advice. 00:16:33.927 --> 00:16:40.687 Forty-two seconds on the two hardest marks of the question — and they are decided by one division. 00:16:40.737 --> 00:16:48.287 There is the block after wave one: Org2, Org1, Org3 at the front, and the free strip behind them. 00:16:48.337 --> 00:16:53.497 Org4 wants five hundred, which rounds to five hundred and twelve. 00:16:53.547 --> 00:17:00.487 Count the doors before you look for them. One thousand and twenty-four over five hundred and twelve is two. 00:17:00.537 --> 00:17:09.487 Two doors: offset zero and offset five hundred and twelve. That is every legal position a slash twenty-three can occupy in this block — there is no third. 00:17:11.117 --> 00:17:17.487 Candidate one: the next free address, offset three hundred and four. The intuitive answer. 00:17:17.537 --> 00:17:26.487 Three hundred and four over five hundred and twelve is nought point five nine. Not whole — and watch what its own mask says: it claims to start at eleven dot ten dot zero dot zero, on top of Org2. 00:17:30.987 --> 00:17:39.937 Candidate two: eleven dot ten dot one dot one twenty-eight. Beautifully round, and the single most popular wrong answer on this question. 00:17:40.537 --> 00:17:48.287 Three eighty-four over five twelve is nought point seven five. Same disease, prettier clothes. 00:17:48.337 --> 00:17:56.197 Candidate three: offset five hundred and twelve. Five twelve over five twelve is one — whole, legal. 00:17:56.247 --> 00:18:05.197 And free, because wave one never crossed eleven dot ten dot one dot forty-seven. Org4 is eleven dot ten dot two dot zero slash twenty-three. 00:18:06.967 --> 00:18:12.457 Eleven dot ten dot one dot one twenty-eight was never slash twenty-three territory. 00:18:12.507 --> 00:18:19.627 It was slash twenty-five territory all along — and that is exactly where Org5 lands. 00:18:19.677 --> 00:18:25.797 Count the doors. Do not feel them. Parent size over block size, and check which of them are free. 00:18:25.847 --> 00:18:32.411 A block that lies about its own front door is not a block. 00:18:32.461 --> 00:18:39.041 The inventory step is one subtraction, and it changes how carefully you have to work. 00:18:39.091 --> 00:18:45.921 Free: eleven dot ten dot one dot forty-eight through eleven dot ten dot three dot two fifty-five. 00:18:45.971 --> 00:18:52.531 One thousand and twenty-four minus three hundred and four — seven hundred and twenty addresses. 00:18:52.581 --> 00:19:01.531 Demanded, after rounding: five hundred and twelve plus one hundred and twenty-eight plus sixty-four. Seven hundred and four. 00:19:02.941 --> 00:19:10.041 Slack: sixteen. And sixteen is exactly one slash twenty-eight, which is the smallest useful unit left. 00:19:10.091 --> 00:19:16.291 So the design has almost no room to be wrong. One misaligned start and a customer is homeless. 00:19:16.341 --> 00:19:24.431 That is what the inventory buys you — it tells you, before you begin, how much care this problem requires. 00:19:24.481 --> 00:19:30.911 And the slack is not waste. It is what a full block looks like when every seam has been squeezed shut. 00:19:30.961 --> 00:19:39.333 The finished design leaves exactly those sixteen addresses, in one clean piece. 00:19:39.383 --> 00:19:43.373 That sixteen is a message from the examiner. 00:19:43.423 --> 00:19:50.483 If the parent block were twice this size, almost any placement would fit, and the alignment rule would look like pedantry. 00:19:50.533 --> 00:19:55.753 You could allocate carelessly and still finish with everyone housed. 00:19:55.803 --> 00:20:03.363 With sixteen addresses of slack, there is no room to absorb a mistake. Every block must land on its own lattice, first time. 00:20:03.413 --> 00:20:12.363 Which is exactly why these numbers were chosen. They are tuned so that the correct method fits, and a plausible wrong method does not. 00:20:13.363 --> 00:20:22.313 When an exam problem has a suspiciously tight margin, that margin IS the question. Notice it, and you know what is being tested. 00:20:24.549 --> 00:20:27.959 Checkpoint two. Paper first. 00:20:28.009 --> 00:20:33.529 One. Round wave two's three requests and give the total demand. 00:20:33.579 --> 00:20:40.919 Two. How much free space is there after wave one, and how much slack does that leave? 00:20:40.969 --> 00:20:49.919 Three. In the request-order counterfactual, exactly which offsets are stranded — and what is the largest block that could still be placed inside them? 00:20:51.079 --> 00:21:00.029 One. Five hundred rounds to five twelve, a slash twenty-three. A hundred to one twenty-eight, a slash twenty-five. Fifty to sixty-four, a slash twenty-six. Total demand seven hundred and four. 00:21:04.099 --> 00:21:13.049 Two. Free is one thousand and twenty-four minus three hundred and four — seven hundred and twenty, from eleven dot ten dot one dot forty-eight. Slack is sixteen. 00:21:15.579 --> 00:21:24.529 Three. Offsets thirty-two to two fifty-five. The largest block that fits is a slash twenty-six at offset sixty-four — sixty-four divides by sixty-four, and sixty-four plus sixty-four is one twenty-eight, still inside the gap. 00:21:33.449 --> 00:21:37.149 Section three. Org4's slash twenty-three. 00:21:37.199 --> 00:21:46.149 The two hardest marks on the final. They are decided by one division, and by refusing to trust the word "next". 00:21:47.416 --> 00:21:55.446 Three addresses are candidates. Two of them are wrong, and one of the two is wrong in a way that looks right. 00:21:55.496 --> 00:22:03.546 First, count. A five-hundred-and-twelve-address block inside a one-thousand-and-twenty-four-address parent has exactly two legal doors. 00:22:03.596 --> 00:22:12.546 One thousand and twenty-four over five hundred and twelve is two. Offset zero, and offset five hundred and twelve. Count them — do not feel for them. 00:22:13.966 --> 00:22:21.616 Candidate one: eleven dot ten dot one dot forty-eight, offset three hundred and four. The next free address. 00:22:21.666 --> 00:22:28.056 This is what the phrase "next free" produces, and it is the intuitive answer. 00:22:28.106 --> 00:22:37.056 Candidate two: eleven dot ten dot one dot one twenty-eight, offset three hundred and eighty-four. Round, tidy, and satisfying. 00:22:37.116 --> 00:22:41.736 This is the single most popular wrong answer on the question. 00:22:41.786 --> 00:22:50.736 Candidate three: eleven dot ten dot two dot zero, offset five hundred and twelve. Not adjacent to anything, and not obviously attractive. 00:22:51.426 --> 00:23:00.376 Before we go on, decide which one you would have written. The answer to that tells you which habit you are still carrying. 00:23:00.849 --> 00:23:05.109 Now execute each one. No judgement, no intuition — one division each. 00:23:05.159 --> 00:23:14.109 Three hundred and four over five hundred and twelve is nought point five nine. Not whole, so it is not a legal start. 00:23:14.839 --> 00:23:23.789 And it is worse than illegal, it is dishonest: run that block's own slash twenty-three mask over its own first address, and the block claims to start at eleven dot ten dot zero dot zero — on top of Org2. 00:23:26.739 --> 00:23:35.689 Three hundred and eighty-four over five hundred and twelve is nought point seven five. Not whole either — same disease, prettier clothes. 00:23:37.469 --> 00:23:46.419 Roundness in decimal is not alignment in binary. One twenty-eight looks round to you; five twelve is what the mask cares about. 00:23:46.959 --> 00:23:52.669 Five hundred and twelve over five hundred and twelve is one. Whole, legal. 00:23:52.719 --> 00:23:59.579 And free — wave one never crossed eleven dot ten dot one dot forty-seven, so there is nothing in the way. 00:23:59.629 --> 00:24:08.389 So Org4 is eleven dot ten dot two dot zero slash twenty-three, running to eleven dot ten dot three dot two fifty-five. 00:24:08.439 --> 00:24:13.519 In one stroke it owns the entire back half of the parent block. 00:24:13.569 --> 00:24:20.809 And there is the sharpest statement of the alignment rule I know: a block that lies about its own front door is not a block. 00:24:20.859 --> 00:24:23.929 Two marks, and they fall out of a single division. 00:24:23.979 --> 00:24:32.929 It does not take the next free address. It takes the only legal one — and "next free" is the habit that costs the marks. 00:24:35.116 --> 00:24:41.316 Underneath all of that is one division, and it is worth stating as a rule. 00:24:41.366 --> 00:24:50.316 Doors equals parent size over block size. A slash twenty-three has two doors in this block. A slash twenty-five has eight. A slash twenty-eight has sixty-four. 00:24:52.326 --> 00:25:00.876 One division tells you how much freedom a block has — and it confirms, again, that the biggest block has the least. 00:25:00.926 --> 00:25:09.876 So check the door count before you place the biggest block. If a block has two doors and one of them is occupied, there is exactly one answer and no judgement involved. 00:25:11.196 --> 00:25:16.226 That is a very comfortable position to be in under exam pressure. 00:25:16.276 --> 00:25:23.886 And if both are occupied, the customer cannot be served. That is not a design failure to argue with. It is arithmetic, 00:25:23.936 --> 00:25:28.136 and the honest answer is to ask the registry for a bigger parent block. 00:25:28.186 --> 00:25:37.136 Count the doors. Do not feel them. That sentence is worth writing at the top of any allocation question you meet. 00:25:39.429 --> 00:25:47.039 This is the whole question as a machine. Every part, and the wrong answers executed rather than described. 00:25:47.089 --> 00:25:56.039 State one is part (a): the parent, and its four facts. One thousand and twenty-four, two five five two five five two five two zero, and the two ends. 00:25:56.979 --> 00:26:02.999 Notice the third octet in the AND panel — three against two fifty-two, and nothing survives. 00:26:03.049 --> 00:26:11.999 State two: wave one's three requests, rounded, and then re-ordered. Their numbering is one, two, three; ours is two, one, three. 00:26:14.279 --> 00:26:23.229 State three places them. Each block carries its own division inside it — zero over two fifty-six, two fifty-six over thirty-two, two eighty-eight over sixteen. 00:26:27.449 --> 00:26:36.119 And the grey tail is named: eleven dot ten dot one dot forty-eight to three dot two fifty-five, seven hundred and twenty addresses. 00:26:36.169 --> 00:26:45.119 State four is the counterfactual. Same customers, allocated in request order, and there is the red band: offsets thirty-two to two fifty-five, two hundred and twenty-four addresses, dead. 00:26:49.979 --> 00:26:55.159 Same total demand. Different order. That is the entire difference. 00:26:55.209 --> 00:27:04.159 State five is the inventory panel: seven hundred and twenty free, seven hundred and four demanded, sixteen of slack. Before anything is placed. 00:27:05.989 --> 00:27:14.939 State six is the finished design. Org4 in the back half, Org5 and Org6 backfilled into the strip, and one hole of sixteen at eleven dot ten dot one dot forty-eight. 00:27:20.609 --> 00:27:24.809 The audit line closes at one thousand and twenty-four. 00:27:24.859 --> 00:27:33.759 And the last state is the wrong answer executed: Org4 placed at the next free address, with the machine refusing to pretend it is a block. 00:27:33.809 --> 00:27:42.759 Three hundred and four over five twelve, and the block's own mask putting it on top of Org2. Open it and try to break it — change the requests, and see which orders survive. 00:27:47.959 --> 00:27:53.769 Checkpoint three, and these are exam questions rather than recall. 00:27:53.819 --> 00:28:02.769 One. How many legal doors does a slash twenty-five have inside a slash twenty-two, and what are the first three offsets? 00:28:03.179 --> 00:28:12.129 Two. Show, in one line each, why eleven dot ten dot one dot forty-eight slash twenty-three and eleven dot ten dot one dot one twenty-eight slash twenty-three are both impossible. 00:28:15.029 --> 00:28:23.979 Three. Org4 is placed at eleven dot ten dot two dot zero slash twenty-three. Give its last address, and say how much of the parent block it owns. 00:28:25.519 --> 00:28:34.469 One. One thousand and twenty-four over one twenty-eight is eight doors. The first three offsets are zero, one twenty-eight and two fifty-six. 00:28:38.399 --> 00:28:47.349 Two. Three hundred and four over five twelve is nought point five nine, not whole; three eighty-four over five twelve is nought point seven five, not whole. Neither offset is a multiple of five hundred and twelve, so neither can be the first address of a slash twenty-three. 00:28:53.259 --> 00:29:02.209 Three. Last address eleven dot ten dot three dot two fifty-five. It owns five hundred and twelve of the one thousand and twenty-four addresses — exactly the back half. 00:29:07.393 --> 00:29:10.953 Section four. The leftovers, and the marks. 00:29:11.003 --> 00:29:19.953 Two organisations still to place, one audit line to write, and a mark scheme that rewards sentences about leftovers. 00:29:21.756 --> 00:29:29.536 With Org4 in the back half, the rest is easy — and that is a sign the hard decision was made correctly. 00:29:29.586 --> 00:29:38.536 Org5 wants one twenty-eight. The free strip runs from offset three hundred and four to five hundred and twelve. Multiples of one twenty-eight in there: three eighty-four. 00:29:39.956 --> 00:29:48.516 Three eighty-four is eleven dot ten dot one dot one twenty-eight — free, legal, and it fits with room behind it. 00:29:48.566 --> 00:29:54.736 The most popular wrong answer on the whole question turns out to be the right address for a different customer. 00:29:54.786 --> 00:30:03.736 Eleven dot ten dot one dot one twenty-eight was never slash twenty-three territory. It was slash twenty-five territory all along. 00:30:04.376 --> 00:30:11.926 Org6 wants sixty-four. Offset three hundred and twenty — three twenty over sixty-four is five, whole. 00:30:11.976 --> 00:30:19.376 Eleven dot ten dot one dot sixty-four slash twenty-six, through one dot one twenty-seven. 00:30:19.426 --> 00:30:28.376 And what is left is eleven dot ten dot one dot forty-eight through one dot sixty-three. Sixteen addresses — exactly the slack we counted before we started. 00:30:30.576 --> 00:30:39.526 Not luck. Sort-and-align squeezed every seam shut, so the leftovers ended up as one clean piece rather than three scraps. 00:30:41.156 --> 00:30:49.106 Here is the complete answer, and I am going to read it the way you should write it. 00:30:49.156 --> 00:30:58.106 Wave one. Org2: eleven dot ten dot zero dot zero slash twenty-four. Org1: eleven dot ten dot one dot zero slash twenty-seven. Org3: eleven dot ten dot one dot thirty-two slash twenty-eight. 00:31:02.516 --> 00:31:08.226 Two fifty-six plus thirty-two plus sixteen — three hundred and four. 00:31:08.276 --> 00:31:17.226 Wave two, backfilled into the old free strip. Org6: eleven dot ten dot one dot sixty-four slash twenty-six. Org5: eleven dot ten dot one dot one twenty-eight slash twenty-five. 00:31:22.236 --> 00:31:30.026 Sixty-four plus one twenty-eight — one hundred and ninety-two, all inside the space wave one left. 00:31:30.076 --> 00:31:39.026 And Org4: eleven dot ten dot two dot zero slash twenty-three, last address eleven dot ten dot three dot two fifty-five. 00:31:39.306 --> 00:31:44.886 Five hundred and twelve addresses, on the only legal door it had. 00:31:44.936 --> 00:31:53.886 Unused: eleven dot ten dot one dot forty-eight through one dot sixty-three. And name it with a prefix — eleven dot ten dot one dot forty-eight slash twenty-eight, 00:31:54.876 --> 00:32:01.526 because those sixteen happen to be aligned, which is what makes them sellable. 00:32:01.576 --> 00:32:10.526 And the audit. Two fifty-six plus thirty-two plus sixteen plus five twelve plus one twenty-eight plus sixty-four is one thousand and eight. Plus sixteen unused: one thousand and twenty-four. 00:32:13.836 --> 00:32:17.306 It balances, and that line is the last thing you write. 00:32:17.356 --> 00:32:26.306 When a written answer can be drawn with no gaps, no overlaps and one honest hole, it is finished. 00:32:26.789 --> 00:32:30.209 The picture is what checks the arithmetic. 00:32:30.259 --> 00:32:39.209 Org2 owns the first quarter. A single slash twenty-four at the front, and the only tenant large enough to be visible from across the room. 00:32:39.839 --> 00:32:48.789 The second quarter is crowded: Org1, Org3, Org6, Org5 — four tenants — and the only vacancy, sixteen addresses at eleven dot ten dot one dot forty-eight. 00:32:53.439 --> 00:33:02.389 And Org4 owns the entire back half. One block, five hundred and twelve addresses, sitting on the only legal door it could have used. 00:33:02.789 --> 00:33:11.739 Draw it. A to-scale bar takes thirty seconds and makes an overlap or a gap visible instantly — faster than any recheck of the arithmetic. 00:33:14.723 --> 00:33:21.573 Now let me show you where the twelve marks actually live, because it changes what you practise. 00:33:21.623 --> 00:33:30.573 Part (a): two marks. N, mask, first, last. Pure ritual — Session eleven, and it should take under a minute. 00:33:31.153 --> 00:33:40.103 Part (b): four marks. Three organisations rounded, sorted, placed and named. Pure ritual — Session fourteen, three times. 00:33:41.703 --> 00:33:50.653 Part (c), Org5 and Org6: two marks. Two more placements in the leftover strip. Session fourteen, twice more. 00:33:52.343 --> 00:34:01.293 Part (c), Org4's slash twenty-three: two marks. The only legal door. This is the separator — where a B becomes an A — and it is one division. 00:34:04.453 --> 00:34:10.673 And the unused range plus the audit line: two marks. Two sentences about leftovers. 00:34:10.723 --> 00:34:16.083 Those are the cheapest marks on the final, and the ones most often left blank. 00:34:16.133 --> 00:34:25.083 Add it up: seven of the twelve are ritual you already own. Two are one division. And two are sentences. Write the sentences. 00:34:27.672 --> 00:34:33.462 The design is finished. Now stand behind the counter and sell what is left. 00:34:33.512 --> 00:34:42.102 There is the finished block, and there is the stock: sixteen addresses at eleven dot ten dot one dot forty-eight. One slash twenty-eight. 00:34:42.152 --> 00:34:45.722 A seventh organisation is on the phone. 00:34:45.772 --> 00:34:53.502 They want twenty. Twenty rounds up to thirty-two, and the largest block in stock is a slash twenty-eight. 00:34:53.552 --> 00:35:02.502 Refused — and notice the reason panel: not "we are out of addresses", but "we have no thirty-two-shaped, thirty-two-aligned space". 00:35:04.282 --> 00:35:10.082 Twelve, though. Twelve rounds up to sixteen, and sixteen is exactly what is on the shelf. 00:35:10.132 --> 00:35:17.672 Served: eleven dot ten dot one dot forty-eight slash twenty-eight, and the stock goes to zero. 00:35:17.722 --> 00:35:22.122 Reset. A customer wanting five rounds up to eight — a slash twenty-nine. 00:35:22.172 --> 00:35:31.122 The shelf splits: one slash twenty-nine sold, one slash twenty-nine left. Watch the inventory line change shape rather than merely shrink. 00:35:32.912 --> 00:35:41.302 Now ten. Ten rounds to sixteen, and only a slash twenty-nine is left. Refused — with eight addresses sitting free. 00:35:41.352 --> 00:35:45.592 The total is not the constraint. The shape is. 00:35:45.642 --> 00:35:54.052 And the sneaky answer: give them eight here and eight from somewhere else. Still refused, and the panel says why — 00:35:54.102 --> 00:36:00.672 that is two blocks, two prefixes, two entries. The customer asked for one network. 00:36:00.722 --> 00:36:08.062 And the rule, which makes every one of these answers obvious before you calculate: quote your stock as prefixes, not as a count. 00:36:08.112 --> 00:36:17.062 "One slash twenty-eight" answers every question that "sixteen addresses" leaves open. Open it and serve a few customers yourself. 00:36:20.045 --> 00:36:26.565 Let me do that last exchange properly on paper, because it is a favourite follow-up part. 00:36:26.615 --> 00:36:32.715 Org7 wants twenty addresses. Twenty rounds up to thirty-two — a slash twenty-seven. 00:36:32.765 --> 00:36:41.175 And the ISP's entire remaining stock is sixteen addresses at eleven dot ten dot one dot forty-eight. 00:36:41.225 --> 00:36:50.175 So the answer is: refused. Not because the ISP is unhelpful, but because there is no slash-twenty-seven-shaped space anywhere in the block. 00:36:51.035 --> 00:36:59.235 Write that reason down. "No space" is worth nothing; "no aligned thirty-two-address space" is the mark. 00:36:59.285 --> 00:37:05.535 And the sneaky wrong answer: give them the sixteen, plus sixteen from somewhere else. 00:37:05.585 --> 00:37:12.015 No. A block is one range with one prefix, and that has been true since Session ten. 00:37:12.065 --> 00:37:18.765 Which is why the ISP's inventory is not "sixteen addresses". It is "one slash twenty-eight". 00:37:18.815 --> 00:37:27.765 Quote your stock as prefixes rather than as a count, and every refusal answers itself before you have to justify it. 00:37:29.378 --> 00:37:36.578 That refusal rests on a fact from Session ten, and it is worth restating from the sales side. 00:37:36.628 --> 00:37:45.578 A prefix names a contiguous, aligned range, and nothing else. That is what a mask does: one AND, one comparison, one answer. 00:37:46.438 --> 00:37:53.028 Two ranges would need two entries and two ANDs. That is two blocks by definition. 00:37:53.078 --> 00:37:59.928 So "sixteen here and sixteen there" is two blocks, not one. The customer asked for one network. 00:37:59.978 --> 00:38:06.908 Two networks is a different, and usually unwelcome, product — they would need a router between them. 00:38:06.958 --> 00:38:15.908 And it is why the hole is genuinely dead stock. Until a customer of sixteen or fewer appears, those addresses cannot be sold to anyone — 00:38:16.158 --> 00:38:19.008 however many addresses are technically "free". 00:38:19.058 --> 00:38:28.008 The mask has to be able to find the block in one instruction. That single sentence is the whole of contiguity, alignment and this refusal. 00:38:30.971 --> 00:38:35.461 Checkpoint four, and this is the last one. 00:38:35.511 --> 00:38:42.791 One. A customer wants twelve addresses. Can the ISP serve them from the finished design? Give the block. 00:38:42.841 --> 00:38:50.761 Two. A customer wants forty. What do you tell them, and why is the total free space irrelevant? 00:38:50.811 --> 00:38:55.951 Three. Write the audit line for the complete design. 00:38:56.001 --> 00:39:04.951 One. Yes. Twelve rounds to sixteen, and there is exactly one slash twenty-eight in stock: eleven dot ten dot one dot forty-eight slash twenty-eight, running to one dot sixty-three. 00:39:08.431 --> 00:39:17.381 Two. Refused. Forty rounds to sixty-four, and the largest block in stock is a slash twenty-eight. The total free space is sixteen — but even if it were larger, the question is whether a sixty-four-shaped, sixty-four-aligned space exists. It does not. 00:39:24.361 --> 00:39:33.311 Three. Two fifty-six plus thirty-two plus sixteen plus five twelve plus one twenty-eight plus sixty-four is one thousand and eight allocated, plus sixteen unused, equals one thousand and twenty-four. It balances. 00:39:42.818 --> 00:39:45.868 Five ways to lose these marks. 00:39:45.918 --> 00:39:50.338 Wrong: allocate them in the order the question numbers them. 00:39:50.388 --> 00:39:59.338 Right: sort descending first. Org2 before Org1, every time — and on this block it is worth two hundred and twenty-four addresses. 00:40:01.008 --> 00:40:06.408 Wrong: Org4 goes at eleven dot ten dot one dot forty-eight, the next free address. 00:40:06.458 --> 00:40:15.408 Right: eleven dot ten dot two dot zero. A slash twenty-three has two doors in a slash twenty-two — count them. Three hundred and four over five twelve is not whole. 00:40:18.808 --> 00:40:24.058 Wrong: eleven dot ten dot one dot one twenty-eight, which is nicely round. 00:40:24.108 --> 00:40:33.058 Right: still no. Three eighty-four over five twelve is nought point seven five. Roundness in decimal is not alignment in binary. 00:40:34.228 --> 00:40:37.718 Wrong: wave two can shuffle wave one along a little. 00:40:37.768 --> 00:40:46.718 Right: read the clause. Nobody moves — and renumbering a live network is not a thing an exam answer is allowed to do. 00:40:46.958 --> 00:40:52.318 Wrong: every organisation has a block, so the answer is complete. 00:40:52.368 --> 00:41:01.318 Right: not until the unused range is named and the audit line is written. Those are two marks of sentences, and they take fifteen seconds. 00:41:03.953 --> 00:41:12.793 I promised at the start that nothing here would be new. Let me collect the whole twelve-mark answer and show you it is true. 00:41:12.843 --> 00:41:21.793 Part (a): one Session eleven ritual. N, mask, AND, plus N minus one. Two marks, under a minute. 00:41:22.283 --> 00:41:30.513 Parts (b) and (c): six Session fourteen rituals. Round, sort, largest first, align — six times, five sentences each. Eight marks. 00:41:30.563 --> 00:41:39.513 Plus two sentences about leftovers: the unused range, and the audit line. Two marks, and the cheapest on the paper. 00:41:40.583 --> 00:41:49.533 Notice how it feels: routine. On the final this page is not a challenge — it is a harvest, and the only way to lose it is to skip the sort. 00:41:54.420 --> 00:41:58.310 Four things you should be able to do now. 00:41:58.360 --> 00:42:07.310 One: run the whole twelve-mark question from a blank page in about fifteen minutes. No notes, and no hesitation at the octet boundaries. 00:42:07.940 --> 00:42:16.890 Two: count a block's legal doors with one division — parent size over block size — and check whether any of them are free. 00:42:17.520 --> 00:42:26.470 Three: say what the ISP still holds, both ways. "Seven hundred and twenty addresses, eleven dot ten dot one dot forty-eight to three dot two fifty-five" — and later, "one slash twenty-eight". 00:42:30.660 --> 00:42:38.090 Four: close with the audit line. Allocated plus unused equals total, always the last thing written. 00:42:38.140 --> 00:42:47.090 Homework is the full sheet from a blank page, timed. Fifteen minutes is exam pace, and the variant sets prove the method transfers. 00:42:50.386 --> 00:42:53.566 Three things before the next session. 00:42:53.616 --> 00:43:00.786 One: the full sheet from blank paper, timed. Fifteen minutes. Not reading the solution — producing it. 00:43:00.836 --> 00:43:07.566 Time yourself honestly and write the number down, because the number is the diagnosis. 00:43:07.616 --> 00:43:15.656 Two: the variant request sets. Forty, two hundred, twenty — then four hundred, one twenty, sixty. 00:43:15.706 --> 00:43:24.656 Sorted and rounded those are two fifty-six, sixty-four, thirty-two, and then five twelve, one twenty-eight, sixty-four. Notice the shape is identical to today's. That is the point. 00:43:29.766 --> 00:43:34.316 Three: read the aggregation pages of section eighteen point four. 00:43:34.366 --> 00:43:43.316 Because we have spent three weeks cutting blocks apart. Next session we glue them back together — and it is the reason the Internet's routers have not drowned. 00:43:43.376 --> 00:43:52.326 If your fifteen-minute run comes in clean, this topic is finished for you. If it does not, the gap is drill, and drill is homework. 00:43:55.192 --> 00:44:01.062 One last thing, because this question does not always arrive in these clothes. 00:44:01.112 --> 00:44:08.182 Disguise one: a different parent. A slash twenty-one, or a slash twenty, instead of a slash twenty-two. 00:44:08.232 --> 00:44:14.702 The offsets get bigger; nothing else changes. Your divisions get one digit longer. 00:44:14.752 --> 00:44:21.322 Disguise two: a different customer count. Four customers, or eight, in one wave or three. 00:44:21.372 --> 00:44:26.872 More rituals, same ritual — and the sort still decides everything. 00:44:26.922 --> 00:44:33.792 Disguise three: a different forbidden clause. "Customer two has already been billed and cannot be moved." 00:44:33.842 --> 00:44:38.102 Same constraint, new wording: wave one is concrete. 00:44:38.152 --> 00:44:47.102 In every disguise the method is identical: round, sort, largest first, align, audit — and name the leftovers. 00:44:49.959 --> 00:44:51.739 That is Session fifteen. 00:44:51.789 --> 00:44:57.519 Round, sort, align, audit — six customers, and zero surprises. 00:44:57.569 --> 00:45:06.519 Part (a) is one Session eleven ritual. Parts (b) and (c) are six Session fourteen rituals. And two of the twelve marks are sentences about leftovers. 00:45:09.679 --> 00:45:18.629 Count the doors — parent size over block size — and never trust the word "next". "Next free" is the habit that costs the two hardest marks on the paper. 00:45:20.069 --> 00:45:27.499 And when the block is full, quote your stock as prefixes rather than as a count, and every refusal answers itself. 00:45:27.549 --> 00:45:34.459 Next session we go the other way: we glue blocks back together, and find out why the routing tables have not drowned. 00:45:34.509 --> 00:45:38.597 I will see you there.