Operating System Functions In relation to virtual memory, describe the terms segment, page and translation lookaside buffer (TLB). [6 marks] The operating system for a microprocessor supports a virtual memory model which implements both segmentation and paging. The only hardware assistance for the virtual memory system in the microprocessor is an on-chip TLB. Outline the data structures held by the operating system. [5 marks] Describe the actions of the operating system in response to an address exception due to not matching the address issued by the processor in the TLB. [5 marks] How can the operating system use access permissions to aid its page replacement policy? [4 marks] 8 Data Structures and Algorithms Describe (a) how to determine whether or not a point is inside a simple plane closed polygon, paying proper attention to awkward cases [6 marks] (b) how, with luck, to exclude large numbers of points from the convex hull of a set of points in the plane, with due consideration of what can go wrong [7 marks] (c) how to compute economically the convex hull of the points that are left after the measures you have described in (b) above [7 marks] 9 Graphics II When scan-converting items for display, a Z-buffer is sometimes used to avoid some sorting. Outline its operation and limitations. [12 marks] The use of an A-buffer will improve matters. Explain why. [8 marks] 4 CST.93.11.5 10 Numerical Analysis I What is meant by the term loss of significance? What is the essential difference between the terms condition and stability in numerical analysis? Define the term machine epsilon and explain why it is an important parameter. [6 marks] Use the recurrence formula cos[(k + 1)] = 2 cos  cos[k]  cos[(k  1)] with starting values cos 0 = 1, cos  =  1 2 +  to evaluate cos 2 and show that loss of significance occurs. [4 marks] Evaluate cos 3 and cos 4, ignoring terms O( 3 ). On this evidence, comment on the stability of the formula. [8 marks] Is the computed value of cos 2 acceptable? Explain your answer. [2 marks] 11 Discrete Mathematics Let A be a non-empty set, and  be a relation on A. What is meant by saying that (A, ) is a partially ordered set? [3 marks] What additional conditions must be satisfied if (A, ) is to form: (a) a totally ordered set [1 mark] (b) a well-ordered set [2 marks] (c) a complete partially ordered set? [3 marks] Suppose now that A is a non-empty set, R a relation on A, and B  A a non-empty subset. Write RB = R  (B  B) for the relation induced on B by R. Show that if (A, ) is a partially ordered set, so also is (B, B). [1 mark] On the set Z = {0, 1, 2, . . .} of integers define the following relations: (i) 6 = S  , the reflexive transitive closure of S = {(n, n + 1) : n  Z} (ii) d = {(m, n) :  q  Z such that mq = n} For each of the set Z and its subsets N = {0, 1, 2, 3, . . .}, N + = {1, 2, 3, . . .} say whether the relations 6 and d induce a partial ordering. Identify instances in which any of the cases (a)-(c) arises, giving your reasons briefly. [10 marks] 5 [TURN OVER CST.93.11.6 12 Proving Programs Correct Explain in detail the method of verification conditions for establishing the truth of partial correctness specifications. [10 marks] Outline a proof that the method is correct.

This question offers with stochastic approaches N(t), t zero where N(t) represents the number of activities within the time c programming language [0, t]. (a) (i) Define a Poisson technique N(t), t 0 of price > zero. [2 marks] (ii) Show that N(t) Pois(t) for every constant t > 0. You may additionally use the end result that limn(1 x/n) n = e x with out evidence. [4 marks] (iii) Let X1 be the time of the first occasion of the Poisson procedure N(t). Show that X1 Exp(). (iv) Now given that N(t) = 1 derive the distribution of the time of the single occasion in [0, t]. [4 marks] (b) Suppose that events of a Poisson method of rate are independently selected at random with chance p > 0. Show that the method of selected occasions is likewise a Poisson manner and establish its price. [2 marks] (c) Describe how your result from component (b) can be used to simulate a nonhomogeneous Poisson method whose rate characteristic (t) is such that (t) for all t 0. [6 marks] 4 CST2.2018.8.5 4 Computer Vision (a) Explain how every of the subsequent equations or expressions can be used for detecting and estimating visible motion in a spatio-temporal photograph series I(x, y, t). Include on your solution the call used to explain every of those preferred classes of motion extraction models: (i) I(x, y, t) t = v I(x, y, t)

(a) A processor's most important memory is usually carried out the usage of DRAM. (i) Describe a regular DRAM cellular. [2 marks] (ii) Show, with the useful resource of a diagram, how DRAM is organised, making reference to devices, ranks, banks and arrays. [4 marks] (iii) Describe the difference between an open-web page and closed-page row-buffer coverage and the types of get entry to styles they advantage. [2 marks] (b) The MOSI cache coherence protocol provides a new owned (O) nation to the fundamental MSI protocol.When a cache protecting a line in M nation snoops a read request from every other cache, it transitions to O nation and forwards the facts to the requestor. Subsequent snoops for read requests also are fulfilled by this owner cache. An owned line is dirty and simplest one cache can maintain a line in O kingdom at any time. (i) Describe the difference between cache coherence and reminiscence consistency. [2 marks] (ii) Draw a country transition diagram for the MOSI protocol, the use of a new motion Forward to suggest facts being forwarded from one cache to some other. [6 marks] (iii) Draw a table showing how the country of a line in one cache limits the states the same line will have in a one of a kind cache. [2 marks] (iv) Give two benefits of adding this greater owned country to the simple MSI protocol.

(a) At the bottom degree, what is the number one purchaser of electrical energy in digital logic today? Give a components for the predicted electricity or energy use for a CMOS gate. [2 marks] (b) A matrix (a 2-dimensional array) is saved on-chip in static RAM. What primary factors make a contribution to the time and energy had to transpose it? [4 marks] (c) Assume now a square matrix is to be held in DRAM. (i) When may it's beneficial to store a couple of-copies of a given matrix in distinctive DRAM banks? [1 mark] (ii) When might or not it's beneficial to keep a couple of-copies of the matrix (or every other example records structure) in one DRAM bank? [2 marks] (iii) One manner to avoid transposing a matrix is truly to keep an annotation that it's been transposed and to then switch over the row and column arguments for every operation. Why would possibly bodily performing the transpose in the end advantage performance? Where would the annotation be held? [2 marks] (d) A computation operates on rectangular matrices of length one zero five one zero five . The internal loop, to be elevated in hardware, has the subsequent simple shape: for (int i= ...) for (int j= ...)

DD[i, j] = ff(SS[i-1, j], SS[i, j-1])

(i) Are there any loop-carried dependencies? What does this suggest for overall performance optimisation? [1 mark] (ii) If the DRAM timings are 11-11-eleven, which means row activation, column activation and writeback each take eleven clock cycles, estimate roughly the minimum time for a naive implementation of the computation. Assume a simple linear facts format. State all in addition assumptions. [6 marks] (iii) What determines whether or not it's miles possible or a great concept to carry out the operation 'in area' (ie. The use of the equal reminiscence for DD and SS)?

[9:41 PM, 5/4/2022] Al.Th.I.Hv: (b) Suppose that events of a Poisson method of rate are independently selected at random with chance p > 0. Show that the method of selected occasions is likewise a Poisson manner and establish its price. [2 marks] (c) Describe how your result from component (b) can be used to simulate a nonhomogeneous Poisson method whose rate characteristic (t) is such that (t) for all t 0. [6 marks] 4 CST2.2018.8.5 4 Computer Vision (a) Explain how every of the subsequent equations or expressions can be used for detecting and estimating visible motion in a spatio-temporal photograph series I(x, y, t). Include on your solution the call used to explain every of those preferred classes of motion extraction models: (i) I(x, y, t) t = v I(x, y, t)

(a) A processor's most important memory is usually carried out the usage of DRAM. (i) Describe a regular DRAM cellular. [2 marks] (ii) Show, with the useful resource of a diagram, how DRAM is organised, making reference to devices, ranks, banks and arrays. [4 marks] (iii) Describe the difference between an open-web page and closed-page row-buffer coverage and the types of get entry to styles they advantage. [2 marks] (b) The MOSI cache coherence protocol provides a new owned (O) nation to the fundamental MSI protocol.When a cache protecting a line in M nation snoops a read request from every other cache, it transitions to O nation and forwards the facts to the requestor. Subsequent snoops for read requests also are fulfilled by this owner cache. An owned line is dirty and simplest one cache can maintain a line in O kingdom at any time. (i) Describe the difference between cache coherence and reminiscence consistency. [2 marks] (ii) Draw a country transition diagram for the MOSI protocol, the use of a new motion Forward to suggest facts being forwarded from one cache to some other. [6 marks] (iii) Draw a table showing how the country of a line in one cache limits the states the same line will have in a one of a kind cache. [2 marks] (iv) Give two benefits of adding this greater owned country to the simple MSI protocol.

(a) At the bottom degree, what is the number one purchaser of electrical energy in digital logic today? Give a components for the predicted electricity or energy use for a CMOS gate. [2 marks] (b) A matrix (a 2-dimensional array) is saved on-chip in static RAM. What primary factors make a contribution to the time and energy had to transpose it? [4 marks] (c) Assume now a square matrix is to be held in DRAM. (i) When may it's beneficial to store a couple of-copies of a given matrix in distinctive DRAM banks? [1 mark] (ii) When might or not it's beneficial to keep a couple of-copies of the matrix (or every other example records structure) in one DRAM bank? [2 marks] (iii) One manner to avoid transposing a matrix is truly to keep an annotation that it's been transposed and to then switch over the row and column arguments for every operation. Why would possibly bodily performing the transpose in the end advantage performance? Where would the annotation be held? [2 marks] (d) A computation operates on rectangular matrices of length one zero five one zero five . The internal loop, to be elevated in hardware, has the subsequent simple shape: for (int i= ...) for (int j= ...)

DD[i, j] = ff(SS[i-1, j], SS[i, j-1])

(i) Are there any loop-carried dependencies? What does this suggest for overall performance optimisation? [1 mark] (ii) If the DRAM timings are 11-11-eleven, which means row activation, column activation and writeback each take eleven clock cycles, estimate roughly the minimum time for a naive implementation of the computation. Assume a simple linear facts format. State all in addition assumptions. [6 marks] (iii) What determines whether or not it's miles possible or a great concept to carry out the operation 'in area' (ie. The use of the equal reminiscence for DD and SS)? [9This question offers with stochastic approaches N(t), t zero where N(t) represents the number of activities within the time c programming language [0, t]. (a) (i) Define a Poisson technique N(t), t 0 of price > zero. [2 marks] (ii) Show that N(t) Pois(t) for every constant t > 0. You may additionally use the end result that limn(1 x/n) n = e x with out evidence. [4 marks] (iii) Let X1 be the time of the first occasion of the Poisson procedure N(t). Show that X1 Exp(). (iv) Now given that N(t) = 1 derive the distribution of the time of the single occasion in [0, t]. [4 marks] (b) Suppose that events of a Poisson method of rate are independently selected at random with chance p > 0. Show that the method of selected occasions is likewise a Poisson manner and establish its price. [2 marks] (c) Describe how your result from component (b) can be used to simulate a nonhomogeneous Poisson method whose rate characteristic (t) is such that (t) for all t 0. [6 marks] 4 CST2.2018.8.5 4 Computer Vision (a) Explain how every of the subsequent equations or expressions can be used for detecting and estimating visible motion in a spatio-temporal photograph series I(x, y, t). Include on your solution the call used to explain every of those preferred classes of motion extraction models: (i) I(x, y, t) t = v I(x, y, t)

(a) A processor's most important memory is usually carried out the usage of DRAM. (i) Describe a regular DRAM cellular. [2 marks] (ii) Show, with the useful resource of a diagram, how DRAM is organised, making reference to devices, ranks, banks and arrays. [4 marks] (iii) Describe the difference between an open-web page and closed-page row-buffer coverage and the types of get entry to styles they advantage. [2 marks] (b) The MOSI cache coherence protocol provides a new owned (O) nation to the fundamental MSI protocol.When a cache protecting a line in M nation snoops a read request from every other cache, it transitions to O nation and forwards the facts to the requestor. Subsequent snoops for read requests also are fulfilled by this owner cache. An owned line is dirty and simplest one cache can maintain a line in O kingdom at any time. (i) Describe the difference between cache coherence and reminiscence consistency. [2 marks] (ii) Draw a country transition diagram for the MOSI protocol, the use of a new motion Forward to suggest facts being forwarded from one cache to some other. [6 marks] (iii) Draw a table showing how the country of a line in one cache limits the states the same line will have in a one of a kind cache. [2 marks] (iv) Give two benefits of adding this greater owned country to the simple MSI protocol.