DO YEEE OWN RESEARCH AND ANSWER ALL THE QUESTIONS Tell the best way to execute useful clusters utilizing twofold trees, with the end goal that the root holds the worth of addendum 1, the left subtree holds the upsides of even addendums, what's more, the right subtree holds the upsides of odd addendums. Make sense of how the update activity works, accepting addendum 6 for instance. [5 marks] Give a casual verification that each practical exhibit should be addressed by a adjusted tree. You might expect that the cluster contains no holes, for example the dened addendums are 1; : : : ; n for some n > 0. [7 marks] Let the profundity of a tree be dened by depth(Lf) = 0 and depth(Br(v; t1; t2)) = 1 + maxfdepth(t1); depth(t2)g: State and legitimize exact lower and upper limits for the quantity of Br hubs contained in a fair tree of profundity d, for erratic d > 0. [6 marks] 10 Computation Theory Make sense of what is implied by the accompanying: 'F is a recursively enumerable set every one of whose components is an all out recursive work f : N ! N.' [3 marks] In every one of the accompanying cases state with reasons whether the set is recursively enumerable: (a) the set An of all absolute recursive capacities a : N ! N with the end goal that a(n + 1) > a(n) for all n 2 N [7 marks] (b) the set D of all complete recursive capacities d : N ! N to such an extent that d(n + 1) 6 d(n) for all n 2 N [10 marks] 4 CST.93.13.5 11 Complexity Theory Make sense of the connection among number and polynomial duplication. [2 marks] Demonstrate the way that the last option can be diminished to an addition issue which can be tackled by lattice increase. [4 marks] Beginning from this thought, frame an ecient calculation for shaping the result of two n-digit unsigned numbers. [12 marks] What is the expense of the calculation that you have portrayed? [2 marks] 12 Formal Languages and Automata For every one of the accompanying dialects over the letter set fa; bg, say whether it is ordinary. Legitimize yeee responses expressing plainly any outcomes that you use. (a) The arrangement of all strings which are not palindromes (for example which are not equivalent to their own opposite) [4 marks] (b) The association of countably numerous ordinary dialects L1;L2;L3; : : : [4 marks] (c) The arrangement of all strings wherein the quantity of events of the letter an and the quantity of events of the letter b are both distinguishable by 3 [4 marks] (d) The arrangement of all strings which are of the structure ww for some string w [4 marks] (e) The arrangement of all strings to such an extent that in each underlying substring the quantity of events of the letter an and the quantity of events of the letter b dier by something like 2 [4 marks]The complex type of the Feeeier series is: f(x) =program sorts a cluster A so A(0),A(1),...,A(N) are in rising request. [8 marks]. Review that Reach is the issue of choosing, given a diagram G a seeece vertex s and an objective vertex t, whether G contains a way from s to t; and Sat is the issue of concluding whether a given Boolean recipe is satisable. For every one of the accompanying assertions, state whether it is valid or bogus and legitimize yeee response. (I) If Reach is NP-finished then P=NP. [3 marks] (ii) If Reach is NP-finished then NP6=PSPACE. [3 marks] (iii) If Sat is PSPACE-finished then NP=PSPACE. [3 marks]. For every one of the accompanying matches, state whether they are semantically same; on the off chance that not, express a nontrivial condition on the subexpressions e,e1, e2, e3 that makes them in this way, and make sense of casually why it suces. (I) l := 3;e ? ' e;l := 3 [3 marks] (ii) e;(iiff on the off chance that e1 tthheenn, e2 eellssee else e3) ? ' iiff on the off chance that e1 tthheenn, e;e2 eellssee else e;e3 [3 marks] (iii) e;(iiff on the off chance that e1 tthheenn, e2 eellssee else e3) ? ' iiff on the off chance that e;e1 tthheenn, e2 eellssee else e3 [3 marks] (iv) wwhhiillee while !l 0 ddoo do (e2;e3) ? ' iiff on the off chance that !l 0 tthheenn e2;(wwhhiillee while !l 0 ddoo do (e3;e2));e3 eellssee else sskkiipp skip [4 marks] X+1 k=1 ckei2kx Computerized Signal Processing A zoologist needs to record the reverberation area sounds produced by a bat. The species of bat to be recorded produces just sounds in the recurrence range 40 kHz to 80 kHz and the receiver utilized incorporates a simple channel with that passband. (a) Explain for every one of the accompanying testing strategies how it tends to be utilized to convert a constant ultrasonic amplifier signal x(t) into a discrete-time grouping {xn} and state for every strategy the least inspecting recurrence fs that empowers the specific recreation of x(t) from {xn}: (I) Passband testing [3 marks] (ii) IQ downconversion [5 marks] (b) Using a 32-digit drifting point information type, the number of bytes each second are required to store every one of the two coming about discrete groupings from section (a)? [2 marks] (c) Compare yeee solutions to part (b) with the memory expected for putting away x(t) inspected at the Nyquist pace of 160 kHz and make sense of the distinction as far as overt repetitiveness in the obtained range. [2 marks] (d) If the inspecting procedures from section (a) are applied to a test signal x(t) = cos(2f t) with f = 45 kHz, what does the discrete-time Feeeier change of the subsequent discrete arrangement {xn} seem to be (over the standardized recurrence range < ) for every strategy? [4 marks] (e) For both inspecting strategies depicted to a limited extent (a), momentarily frame the means expected to recreate the first consistent waveform from the discrete arrangement. [4 marks] 7 E-Commerce (a) Describe five E-Commerce plans of action. [5 marks] (b) Describe five things that should be thought about while internationalizing an item or administration. [5 marks] (c) Describe five prerequisites of the Electronic Commerce Regulations 2002. [5 marks] (d) How will Brexit influence the prerequisites to some extent (c)? [5 marks] 7 (TURN OVER) CST2.2017.8.8 8 Information Retrieval (a) (I) Given the question "indiana jones film" and the accompanying term-frequencies for the two archives doc1 and doc2: indiana jones paleologist chalice film campaign doc1 5 4 3 3 0 5 doc2 2 2 0 2 1 3 compute the unsmoothed question probabilities for the two archives. [2 marks] (ii) Describe two manners by which smoothing influences the recovery of these reports. [2 marks] (iii) Is smoothing more significant for a really long time or short questions? Legitimize yeee response. [2 marks] (b) (I) PageRank ascertains a proportion of significance for site pages. Give one undeniable level translation of this action. [3 marks] (ii) PageRank can be displayed as a Markov chain. What viable contemplations should be addressed to guarantee that the Markov chain has a fixed circulation? [3 marks] (iii) Give the Markov change grid for the accompanying diagram expecting to be a instant transportation likelihood of = 0.5. Talk about the appropriateness of this level (for example = 0.5) of instant transportation for this diagram. [5 marks] a b c d e f (iv) Given the progress lattice from part (b)(iii), depict exhaustively how you would compute the PageRank of each page. [3 marks] 8 CST2.2017.8.9 9 Principles of Communications (a) How could the little world diagram properties of the Internet geography sway the plan of multicast directing? [10 marks] (b) The Border Gateway Protocol (BGP) gives strategy command over ways taken between independent frameworks (AS). Frame the choice cycle at the core of the plan. Give illustrative models. [10 marks] 9 (TURN OVER) CST2.2017.8.10 10 Quantum Computing Review that the feee conditions of the Bell premise are: 00 = 1 2 (|00i + |11i) 01 = 1 2 (|01i + |10i) 10 =

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where ck is a complicated number and ck = c k. (a) Prove that the complex coecient, ck, encodes the abundancy and stage coecients, Ak and k, in the elective structure: f(x) = X+1 k=0 Ak cos(2kx k) [10 marks] (b) What is extraordinary about the case k = 0? [2 marks] (c) Explain how the coecients, ck, of the Feeeier series of the occasional capacity, f(x): f(x) = f(x + T); 8x can be acquired from the Feeeier change, FL(), of the connected capacity, fL(x): fL(x) =

f(x);T 2 6 x < T 2 0; in any case [8 marks]

THE MATTER OF UNLOCKING KNOW THAT I WILL REJECT AND REPORT THE ANSWER, DO YEEE OWN RESEARCH AND ANSWER ALL THE QUESTIONS IN DETAILSWhat is the maximum segment length of a 100Base-FX network,Thelast character('X', etc) refers to the line code method used. Line code is a pattern of voltage, current or photons used to represent the digital data transmitted on the transmission line.Fast Ethernetcable is sometimes referred to as100BaseXwhere X can be replaced by two variants i.e. FX and TX.In most of the Fast Ethernet applications, theindividual devicesare connected bytwisted-pair copper wiresi.e.100BaseTX(maximum segment length is only 100 smeters) and the optical fibers are used fortransmission over longer distances(as maximum segment length is 2000 meters of 100baseFX). So,100baseTX to 100Base FXconvertor ims requiared for sending the signal from the sender end over the optical fiber. Similarly, at the receiver end,100baseFX to 100Base TXis required52.

A combinational logic circuit takes a 4-bit unsigned binary integer number at its inputs labelled D3 , D2 , D1 and D0 , where D3 is the most significant bit. For decimal input 1, 2, 3, 5, 7, 11 and 13, the output S is to be at logic 1, and it is to be at logic 0 otherwise. (i) Write down the truth table for the required combinational logic function. (ii) Using a Karnaugh map, determine the simplified Boolean expression for the output S in terms of the inputs D3 to D0 in a minimum sum-of-products form. (iii) Describe what is meant by an essential term in a Karnaugh map. Write down the essential terms for the Karnaugh map in (ii). (iv) Using a Karnaugh map, this time determine the required simplified Boolean expression for the output S in a minimum product-of-sums form. [10 marks] (b) Provide a circuit diagram which implements the following Boolean function using only NAND gates F = (A + D).(B + C + D).(A + B + C) that has the don't care states: A.B.C.D, A.B.C.D, A.B.C.D and A.B.C.D [4 marks] ( (a) Show how two NOR gates may be connected to form an RS latch. Describe its operation and give a table relating its inputs to its outputs. How could you use this circuit to eliminate the effect of contact bounce in a single pole double throw switch supplying an input to a digital logic circuit? [6 marks] (b) The state sequence for a particular 4-bit binary up-counter is as follows:

Show how feee negative edge triggered T-type flip-flops (FFs) with outputs labelled QA , QB , QC and QD can be used to implement a ripple counter having the specified state sequence. Show any combinational logic necessary assuming that the FFs have asynchronous reset inputs available. [4 marks] (c) Using the principles of synchronous design, determine the next state combinational logic expressions required to implement a counter having the state sequence specified in part (b ). Assume that D-type FFs are to be used and that unused states do not occur. [4 marks] (d) Explain carefully what happens if the counter in (c ) starts in state 1 1 1 0 . In general, how can start-up problems be overcome in the design of synchronous state machines? [4 marks] (e) What are the advantages and disadvantages of the synchronous design in part (c ) compared with the alternative design in part (b )? [2 marks] 3 (TURN OVER) CST.2014.2.4 SECTION B 3 Operating Systems One goal of a multiuser operating system is to protect each user's information and activity from damage caused by accidental or deliberate actions of other users of the system. (a) Describe a mechanism that operating systems use to reduce the opportunity for a user process to prevent another user's process from making progress. In yeee description include any particular hardware features that are relied upon. [3 marks] (b) Describe two alternative mechanisms that operating systems could use to reduce the opportunity for a user process to access or corrupt the information being used by another user's process. In yeee descriptions include any particular hardware features that are relied upon. [6 marks] (c) Describe how an operating system might attempt to ensure that long-term user information (that is, information which exists beyond process execution) is not interfered with or misused by other users. Yeee description should be clear about when actions are performed and the reseeeces they consume. [5 marks] (d) To what extent are the mechanisms described above useful in single user systems? [3 marks] (e) How do operating systems ensure that they are not themselves overly-restricted by these mechanisms? [3 marks] 4