Sketch the design of an 8-bit to 2-bit multiplexer. [5 marks]…
Question Answered step-by-step Sketch the design of an 8-bit to 2-bit multiplexer. [5 marks]… Sketch the design of an 8-bit to 2-bit multiplexer. [5 marks] Suppose you had to implement an arbitrary function of seven variables and were provided with nine 8-bit to 1-bit multiplexers and an inverter. How would you implement the function?Digital Electronics The “Wacky Flip-Flops Company” has sent you the following datasheet with schematics of their latest flip-flops. For each flip-flop, determine the truth table, label the inputs and outputs (e.g. “input U is the clock”) and name the flip-flop (e.g. “it is a T-type flip-flop”). “Wacky Flip-Flops Company” Datasheet E F G H J K P R Q S T (a) (c) (d) (b) N L M [5 marks each] 4 CST.2005.2.5 SECTION C 4 Probability (a) Given a random variable X distributed Geometric(p) one has: P(X = r) = q r p where p + q = 1 By using a suitable generating function, derive expressions for the expectation and variance of X. [6 marks] (b) A computer game proceeds in a sequence of steps and, at each step, the contents of a two-bit random number generator are inspected. Each bit is 1 with probability p and 0 with probability q where p + q = 1. The two bits are independent. If the two bits differ (as 01 or 10) the game ends but if the two bits are the same (as 00 or 11) the game proceeds to another step. Accordingly, the game could be as short as a single step but it could last many steps. Let X be a random variable whose value r is the length of a game measured in steps. The game cannot end at step 0 so P(X = 0) = 0. (i) Derive an expression for P(X = r). [5 marks] (ii) Show that X? r=0 P(X = r) = 1. [4 marks] (iii) Derive an expression for the expected length of a game measured in steps. [5 marks] 5 [TURN OVER CST.2005.2.6 5 Probability By repeatedly dropping a knitting needle onto a floor constructed from parallelsided floor boards one may estimate the value of ?. Suppose the needle has unit length and the boards have unit width. After each drop the position of the needle may be specified by the values of two independent random variables: ? is the (acute) angle that the needle makes with the joints of the boards and it may be assumed that ? is distributed Uniform(0, ? 2 ). [It is not necessary to consider values of ? in the other three quadrants.] y is the distance of the centre of the needle from the nearest joint between two boards and it may be assumed that y is distributed Uniform(? 1 2 , + 1 2 ). (a) Sketch sufficient of the ?-y plane to show the whole of the region R which corresponds to the needle crossing a joint. Deem such a crossing to be a hit and show that the probability of a hit is 2/? and, therefore, the value of ? may be estimated experimentally by the formula 2 × drops/hits. [8 marks] (b) Suppose the needle is dropped n times. Let X be a random variable whose value is the number of hits. X is distributed Binomial(n, 2/?). Give expressions for the Expectation E(X) and the Variance V(X). [2 marks] (c) Let ?e(n) denote the estimated value of ? when the number of hits is two standard deviations below the mean. Show that for ?e(n) < ? + 0.1 to hold, the number of drops n must be such that n > 2(? ? 2)(? + 0.1)2 0.01 [10 marks] 6 CST.2005.2.7 SECTION D 6 Professional Practice and Ethics (a) What is the defining characteristic of consequentialist theories in ethics? How can consequentialist theories differ? Identify at least two problems with consequentialist theories. [4 marks] (b) Give at least three functions of professional organisations and say why these functions are managed by the professional organisation (rather than some other organisation such as the government or universities). [6 marks] (c) Name two possible health problems that may arise in the IT industry and how they can be averted. [4 marks] (d) Give one good reason why it is (or why it is not) reasonable to require members of a professional body to report back to the professional body significant violations of professional conduct on the part of another member. [1 mark] (e) In addition to technical measures (passwords, encryption etc.) what more do organisations have to do to maintain information security? [2 marks] (f ) Under the Data Protection Act, are your rights violated if an organisation (e.g. your college) gains access to your e-mail, prints it out and distributes it to members of staff? [1 mark] (g) What are the two main kinds of law that are used to provide intellectual property protection for software? [2 marks] 7 Software Engineering I A car manufacturer wishes to save weight and improve reliability by replacing most of the vehicle’s wiring harness with a local area network. Systems such as engine management, anti-lock braking, traction control and stability control will thus share common platform components. Your task is to ensure that the safety of these systems, and of the vehicle electronics overall, is not impaired by this upgrade. (a) Describe the methodology you would adopt for the project, and justify your choice. [10 marks] (b) How would you then ensure that subsequent development of these subsystems – which you should assume are supplied by different subcontractors – does not compromise vehicle safety? [10 marks] 7 [TURN OVER CST.2005.2.8 8 Software Engineering II You are asked to design a new product – a speed and distance computer to be mounted on the handlebars of a bicycle. The hardware includes two control pushbuttons, an LCD screen and a rotation sensor on the bicycle wheel. The device will have three normal operating modes: display of the current speed and distance travelled today; a graph of distance travelled on each day of the week; and a graph of average speed plotted against day of the week. It will be powered by stored energy from the rotation sensor. As stored energy becomes depleted, power management functions should first save data to non-volatile memory, then turn off the screen, and as a last resort shut down clock functions. (a) Draw preliminary diagrammatic software design models (i.e. not complete designs) suitable for: (i) presenting functionality to a potential customer; (ii) planning data storage and manipulation; (iii) analysing power management modes; and (iv) defining the procedure for plotting the speed graph. [3 marks each] (b) For each of these models, name a different technique that could be used to verify that it is correct. [4 marks] (c) For part (a)(iv) only, suggest good names for four variables that would be used in implementing the procedure, indicating what role each variable plays. [4 marks] 8 CST.2005.2.9 9 Regular Languages and Finite Automata (a) Languages L1, L2 over alphabets ?1, ?2 are accepted by deterministic finite automata M1, M2. Show how to construct a deterministic finite automaton M from M1 and M2 that accepts the intersection L1 ? L2 of the two languages. What happens if M1 and M2 are non-deterministic? [10 marks] (b) A context-free grammar has a set of terminals {0, 1, ?}, a set of non-terminals {N, P}, where N is the start symbol, and productions given by the following BNF. N ::= 0 | P | ? P P ::= 1 | P 0 | P 1 (i) Give a deterministic finite automaton that accepts the language generated by this context-free grammar. [4 marks] (ii) Give a regular expression that determines the same language. [1 mark] (iii) What is meant by regular context-free grammars and what is their connection with regular languages? Is the context-free grammar given above regular? [5 marks] 9 CST.2005.2.10 10 Structured Hardware Design A design is required for a battery-operated device that replays stored music through headphones. (a) What are the properties of EAROM memories (also known as Flash)? [4 marks] (b) Given that CD quality music is sampled at 44 ksps with 16 bits per stereo channel, and that MP3 compression will be used at a ratio of about 5 to 1, and that three hours storage capacity is required, how much EAROM memory is needed? [4 marks] (c) Ignoring partition of function between silicon chips, sketch a block diagram for a basic design, including any connections, controls and features that are likely to be needed. [8 marks] (d) How many custom chips should be developed for this product and what other custom toolings should be used for a profitable run of 250K production units? 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