What problems could arise here, and how could they be overcome? [6 marks] 6 Numerical Analysis I (a) For Single Precision in the IEEE binary floating-point standard (IEEE 754) the precision is defined as 24, and the exponent requires 8 bits of storage. With reference to IEEE Single Precision, explain the terms exponent, significand, precision, sign bit, normalised number, denormal number. [6 marks] (b) Explain the term hidden bit. What are the values of the hidden bit for normalised and denormal numbers? How is the exponent stored and why? How are the exponent, significand and sign bit arranged in memory? [4 marks] (c) Let x denote the floating-point representation of a number x. Define the terms absolute error (x) and relative error (x) in representing x. How are x and x related? Define machine epsilon (m). [3 marks] (d) Assume x = y = z = m. Using worst-case analysis, estimate xy, xy. Find an expression for w where w = z xy. [4 marks] (e) Working to 4 significant decimal digits only, compute w when x = 2.018, y = 2.008, z = 4.058. Given m ' 0.5 103 , how many significant decimal digits of w can be relied on? [3 marks] on of a Turing machine that is specified by a quintuplet description. [4 marks] (c) Define the configuration of a Turing machine at step t, and establish equations that specify the configuration of a k-symbol Turing machine at step (t + 1) in terms of the configuration at the previous step t. [6 marks] (d) Explain how you would use your equations to simulate a specific Turing machine by a register machine whose program encodes the quintuplet description. To what extent does this support Turing's Thesis? [Explicit program for a register machine is not required.] [8 marks] 8 Computer Graphics and Image Processing Describe an algorithm for performing scan conversion of a set of 3D polygons, including details of clipping, projection, and the underlying 2D polygon scan conversion algorithm. You may assume that you are given the colour of each polygon and that no lighting calculations are required. Please state any additional assumptions that you need to make. Ray tracing is not an acceptable answer to this question. [20 marks] 5 [TURN OVER CST.2004.3.6 9 Introduction to Security (a) Explain briefly mechanisms that software on a desktop computer can use to securely generate secret keys for use in cryptographic protocols. [5 marks] (b) Give two different ways of implementing residual information protection in an operating system and explain the threat addressed by each. [5 marks] (c) Consider the standard POSIX file-system access control mechanism: (i) Under which conditions can files and subdirectories be removed from a parent directory? [2 marks] (ii) Many Unix variants implement an extension known as the "sticky bit". What is its function? [2 marks] (iii) On a POSIX system that lacks support for the "sticky bit", how could you achieve an equivalent effect? [2 marks] (d) VerySafe Ltd offer two vaults with electronic locks. They open only after the correct decimal code has been entered. Design for the Data Structures and Algorithms (a) Describe how the Lempel Ziv text compression algorithm works, illustrating your answer by deriving the sequence of numbers and corresponding bit patterns it would generate when applied to a string starting with the following 24 characters: ABCDABCDABCDABCDABCDABCD ... You may assume that the initial table is of size 256 (containing bytes 0 to 255) and that the codes for "A", "B", "C" and "D" are 65, 66, 67 and 68, respectively. [12 marks] (b) Estimate how many bits the algorithm would use to encode a string consisting of 1000 repetitions of the character "A". [8 marks] 4 Comparative Programming Languages (a) Discuss to what extent a programmer can expect a program that conforms to a standard to generate identical results when run under different conforming compilers on different machines. [6 marks] (b) ALGOL 60 provided call by value and call by name, Pascal provided call by value and call by reference, and ALGOL-W provided a variety of calling methods including call by result and call by value-result. Briefly describe the calling mechanisms just mentioned and discuss why most modern programming languages provide only call by value. [8 marks] (c) Discuss the reasons why languages such as Fortran, Algol and PL/I designed in 1950s and 1960s are less widely used than languages designed in the last 20 years. [6 marks] 3 [TURN OVER CST.2004.3.4 5 Operating Systems II (a) What problem do real-time scheduling algorithms try to solve? [2 marks] (b) Describe one static priority and one dynamic priority real-time scheduling algorithm. You should discuss the issue of admission control, and comment on the data structures that an implementation would need to maintain and on how these would be used to make scheduling decisions.are a data structure protected by a mutual exclusion lock. (i) What scheduling problem could arise here? [2 marks] (ii) How could this problem be overcome? [2 marks] (d) The designer also wishes the real-time system to use demand paged virtual memory for efficiency. What problems could arise here, and how could they be overcome?

Software Design #1: Costs $30,000, and will facilitate profits of $8,000/year

Software Design #2: Costs $40,000, and will facilitate profits of $9,500/year

Which Software Design should they choose?

Enter the NPV of the Software Design they should choose:

Why do we learn Software Design Patterns? 3. (2005) What is a Software Design Pattern?

(e) Give a brief and rudimentary clarification of the standards of how the language coming about because of part (b) may be utilized to make a sentence structure analyser taking a token stream as information (by means of calls to work lex()) and giving as result an theoretical language structure tree relating to part (d). Notice both transcribed also, consequently created grammar analysers. (f ) Summarize any issues connected with left-or right-cooperative administrators in the two methods (in executing the parser and in developing the apparatus) you illustrated to some degree (e).

a) Software design is an important process in software development lifecycle. However, a lot of software developer/house tends to ignore the process. Therefore, provide and explain 2 motivations on software design

b)Two major activities of the software design process include Software Architecture and Detailed Design. Demonstrate on how these two activities being executed? (1) Do you design software when you "write" a program? What makes software design different from coding? (2) What is the goal of software design? What would be different if developers went straight to coding without adhering to software design principles? (iii) Objects: Electronic health records (EHRs) in a nationwide service. Policy: The owner (patient) may read from its own EHR. A qualified 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 access. A candidate has no access until after the marks have been published. [8 marks each] 4 CST.2004.13.5 5 Computer Graphics and Image Processing (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] (b) 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] (c) Explain what specular and diffuse reflection are in the real world. State and explain equations for calculating approximations to both in a computer. [8 marks] 5 [TURN OVER CST.2004.13.6 6 Compiler Construction (a) Explain the differences (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] (c) A new programming language has the notion of "statically scoped exceptions" in which the program exception foo; void f() { try { void g() { raise foo; } try { g(); } except (foo) { C2 } } except (foo) { C1 } } would execute C1 rather than C2 as the former was in scope at the raise point. By analogy with statically scoped variables, or otherwise, explain how such exceptions might be implemented on a stack. [10 marks] 6 CST.2004.13.7 7 Artificial Intelligence In the following, N is a feedforward neural network architecture taking a vector x T = ( x1 x2 xn ) of n inputs. The complete collection of weights for the network is denoted w and the output produced by the network when applied to input x using weights w is denoted N(w, x). The number of outputs is arbitrary. We have a sequence s of m labelled training examples s = ((x1, l1),(x2, l2), . . . ,(xm, lm)) where the li denote vectors of desired outputs. Let E(w; (xi , li)) denote some measure of the error that N makes when applied to the ith labelled training example. Assuming that each node in the network computes a weighted summation of its inputs, followed by an activation function, such that the node j in the network computes a function g w (j) 0 + X k i=1 w (j) i input(i) ! of its k inputs, where g is some activation function, derive in full the backpropagation algorithm for calculating the gradient E w = E w1 E w2 E wW T for the ith labelled example, where w1, . . . ,