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Explain to your colleague why you might not be able to lend them…Explain to your colleague why you might not be able to lend them one ofyour /64 allocations, even though the /64 blocks (provided to you by yourISP) are each globally routable addresses. [2 marks](b) A local area network may carry several different LANs simultaneously; such anetwork would be designated for known sets of HomePlug devices.Describe a physical line coding approach for the HomePlug devices that: allowstwo or more simultaneous virtual local area networks to fairly share the samephysical channel, but does not permit trivial interception of network traffic.Outline your approach along with its benefits and drawbacks, comparing it withthe simplest use of VLAN tags in EthernetThe network illustrated above represents an Ethernet Layer-2 network that usesA na¨ive user translates the following C code: extern int h(int *x, int flag); int f(int *x) { return h(x, x[0]); } int g(int *x) { return h(x + 2, (x[5]+x[6]) | 1); } into the following assembly code for the MIPS R2000: .set noreorder .globl f,g ; export f,g (implicitly import ‘h’) f: lw $5,0($4) ; r4 holds ‘x’, load *x as 2nd argument j h ; tail-call to h g: add $4,$4,8 ; r4 holds ‘x’, load &x[2] as 1st argument lw $5,12($4) ; r4 holds ‘x+2’, load x[5] as 2nd argument lw ,16($4) ; r4 holds ‘x+2’, load x[6] to a temporary add $5,$5,$6 ; do the ‘+’ … or $5,$5,1 ; … and the ‘|’. j h ; tail-call to h Each line of the above assembler program is individually a legal instruction or pseudo-instruction with valid comment. Explain in detail the effect of calling the assembler version of f with a suitable argument including a C function which exactly corresponds to the effect of the assembler version of f. [5 marks] State the purpose of the .set noreorder directive. [2 marks] Explain how the programmer has failed to understand the R2000 instructions and give a correct translation of the C code into assembly code (do not suggest removing the .set noreorder as part of the answer). [5 marks] Explain briefly the origins of the errors (in both f and g) in terms of MIPS R2000 architecture. [5 marks] How might knowing the first instruction of the compilation of h() affect your answer? [3 marks](a) Compare and contrast the problems experienced in developing the London Ambulance control system with those of the Cambridge University financial accounting system (CAPSA). [6 marks] (b) For each of these systems, describe software engineering techniques that might have been used to avoid the problems. Identify advantages and disadvantages of these techniques.An undirected network is an undirected graph in which each edge u ? v has an associated capacity c(u ? v) > 0. Let there be a source vertex s and a sink vertex t. We wish to find the maximum flow from s to t such that on every edge u ? v either there is flow u ? v, or there is flow v ? u, or there is no flow at all. It is not allowed to have flow in both directions simultaneously. The flow on an edge, whichever direction it is in, must not exceed capacity. We can write the flow constraints in mathematical notation as min f(u ? v), f(v ? u) = 0 and max f(u ? v), f(v ? u) = c(u ? v) where f(u ? v) is the flow from u to v on edge u ? v. Note that this differs from the conventional Ford-Fulkerson setup, in which each directed edge has a capacity constraint. (a) Define the value of a flow. State the flow conservation equation. [2 marks] (b) Give an algorithm for finding a maximum flow. [6 marks] (c) Prove that your algorithm returns a valid flow. [4 marks] (d) Prove that your algorithm returns a maximum flow. [4 marks] (e) Define the capacity of a cut in an undirected network. Show that the maximum flow value is equal to the minimum cut capacity. [4 marks] [Hint: You may refer to code from lecture notes without repeating it in your answer. You may quote without proof any theorems from lecture notes.] Why would an IPv6 based provider allocate four /64 networks for yourpremises when each /64 represents 264 addresses? [2 marks](ii) A colleague has IPv6 with another provider; they only allow one /64 foreach domestic installation. In the past your colleague has used a NAT andmany IPv4 private address blocks, but keenly adopted IPv6 permittingthem to upgrade their home network. They are now using blocks of theallocated /64 and a router in their home to interconnect the subnets.Not everything is working as they hoped; for example, sometimes IoTdevices can’t connect to the Internet to update and your colleague cannot connect to their front-door camera when at work.Suppose set S has m elements and set T has n elements. Give explicit formulaeinvolving m and n only for the functionsf(m, n) = |B|/|I| and g(m, n) = |B|/|S ?T|where B and I are the subsets of S ? T consisting of those functions which are4 Operating SystemsDescribe the various functions involved in interrupt handling. Indicate the hardwareand software that might be involved in their implementation. [7 marks]Discuss the interaction of interrupt-driven software and process scheduling in anoperating system. [3 marks]2A path through the graph is represented by a bool list with true and falseindicating left and right edges, respectively.Define the function last : G -> bool list -> int that will yield, for a givengraph, the identity of the vertex reached by following the given path from the root.[3 marks]In a new application, where last is repeatedly called, it is required for it to returnboth the identity of the last vertex and a count of how often this particular vertexhas been returned. Define a new version of the datatype G, containing mutablevalues, that could be used. [3 marks]Illustrate the use of this datatype by defining the new versions of mkgraph and5 Foundations of Computer ScienceNoughts and Crosses is a game played by two players (O and X) on a board withnine positions numbered as follows:1 2 34 5 67 8 9The players place their marks (O and X) in unoccupied positions on the board untilthe game is complete. A completed game is when either(a) there is a straight line of three Xs giving a win for X, or(b) there is a straight line of three Os giving a win for O, or(c) all nine positions are occupied, in which case the game is drawn.O is the first player to move.It is required to construct an ML structure representing the tree of all possiblegames. Each node of the tree should represent a reachable board state, with theroot being the empty board, and the leaf nodes corresponding to won, lost or drawngames.Define the ML datatype tree that you would use to represent this game tree.[3 marks]Define the function mktree : unit->tree to construct the complete game tree,explaining carefully how it works. There is no need for your implementation to beefficient in either space or time. [10 marks]Briefly discuss ways in which your implementation of mktree could be made moreefficient. [4 marks]Define a function Owins : tree->int which when applied to the complete treewill yield the number of distinct games in which O wins. [3 marks]Describe an algorithm (other than thresholding) which will convert a greyscale image (8 bits per pixel) to a bi-level black and white image (1 bit per pixel), with the same number of pixels, while retaining as much detail as possible. [8 marks](b) Explain what specular and di?use re?ection are in the real world. State and explain equations for calculating approximations to both in a computer. [8 marks]The IA-64 architecture includes a number of instruction set features that are intended to allow compilers to generate code that will execute with fewer pipeline stalls.Explain how four of the following ?ve features operate, and how they could be used by a compiler to improve performance relative to more conventional instruction sequences.(a) Register windows for procedure call linkage.(b) Not a Thing (NaT) “poison” bits associated with registers.(c) Address aliasing table (ALAT) for load data speculation.(d) Register ?le rotation.(e) Parallel compares.[5 marks each]2 Digital Communication II(a) Describe the operation of the TCP congestion control scheme, covering the two phases of slow start, congestion avoidance and the triggers of duplicate ack and timeout that set it in train. [10 marks](b) A computer is connected to the Internet via a wireless link using the packet service from the mobile phone company. This o?ers 30 kbps data rate, but has a widely varying round-trip time across the wireless hop from the computer to the next hop in the backbone of between 700 milliseconds and 1.1 seconds. It also has an average packet loss rate of 25%. Using time-sequence diagrams to illustrate the fate of data packets and acknowledgements, show the impact that this has on the throughput that a typical TCP implementation would achieve. [10 marks(a) Describe an e?cient algorithm to determine whether two ?nite line segments in a plane intersect. You may assume that the end points of each line are given as x-y coordinates. [8 marks](b) Describe in detail an e?cient algorithm to ?nd the convex hull of a set of points lying on a plane. Show that the complexity of the Graham scan used in the algorithm is O(n) and that the algorithm as a whole has complexity O(nlogn). [8 marks](c) Discuss how it is possible to eliminate many of the points before the convex hull algorithm is entered. [4 marks]2 Computer DesignThe ARM processor allows the second operand to be shifted by an arbitrary amount. In order to improve the performance, a six-stage pipeline is proposed with the following stages:instruction decode and shiftexecutememory register fetch register fetch operand 2 access write back(a) What are control hazards and how could they be resolved in the above pipeline? [4 marks](b) What are data hazards and how could they be resolved in the above pipeline? [4 marks](c) What are feed-forward paths and where could they be added to the above pipeline to improve performance? [6 marks](d) Why might a branch instruction result in pipeline bubbles and how many bubbles will appear in the above pipeline as a result of taking a branch instruction? [6 marks]3 Digital Communication I(a) De?ne the terms latency and capacity as applied to communication channels. [2 marks](b) Is there a strict relation between the two? [1 mark](c) Show how the latency of a channel can have a direct e?ect on the capacity of a higher-layer channel which uses it. [10 marks](d) How can the capacity of the higher-layer channel be improved (keeping the characteristics of the underlying channel unchanged)? [4 marks](e) In what circumstances might these improvements have only limited bene?t? [3 marks]A network-based service manages persistent objects. The service must enforce an access control policy to protect the objects.(a) Discuss how this access control might best be implemented for the following example of objects and policy components:Objects: Files in a University Department’s ?le service, operating behind a ?rewall. Policy: The owner may specify read, writ and execute rights in terms of principals and groups. [4 marks](b) Discuss how this access control might best be implemented for two of the following examples:(i) Objects: Files in a commercial, distributed, Internet-based ?le service. Policy: The owner may authorise other principals to download the ?le.(ii) Objects: Sales data relating to a company. Policy: Those employed in the Sales Departments of all branches of the company worldwide may read the data.(iii) Objects: Electronic health records (EHRs) in a nationwide service. Policy: The owner (patient) may read from its own EHR. A quali?ed and employed doctor may read and write the EHR of a patient registered with him/her.(iv) Object: The solution to online coursework. Policy: The coursework setter has read and writ access. A candidate has no access until after the marks have been published.[8 marks each](a) Explain why display devices appear to be able to reproduce (almost) all the colours of the spectrum using only red, green and blue light. [4 marks](a) Explain the di?erences (illustrating each with a small program) between(i) static and dynamic binding (scoping); [4 marks](ii) static and dynamic typing. [2 marks](b) Java is sometimes said to be “dynamically typed” in that a variable whose type is (class) C can be assigned a value of (class) D provided that D extends C; conversely a variable of type D can be assigned a value of type C using a cast. By considering storage layouts, explain why the former assignment is always valid and the latter sometimes invalid. [4 marks]6 Foundations of Computer ScienceA rooted directed graph has vertices identified by integers. Each vertex v has a leftsuccessor given by left(v) and a right successor given by right(v), where leftand right are ML functions of type int->int. The graph contains the root andall vertices reachable by paths from the root.Define a datatype G that could be used to represent such a graph with given root,and left and right functions, and define a function mkgraph(root, left, right)that can create values of type G. Show that   Computer ScienceEngineering & TechnologyObject-Oriented Programming HIST 143

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