(a) The parameters for IEEE Single Precision are: = 2, p = 24, emin…
Question Answered step-by-step (a) The parameters for IEEE Single Precision are: = 2, p = 24, emin… (a) The parameters for IEEE Single Precision are: ? = 2, p = 24, emin = ?126,emax = 127. Explain the terms significand, sign bit, exponent, normalisednumber, denormal number, hidden bit, precision as used in IEEE SinglePrecision. [7 marks](b) Let ? represent any of the operations + ? ? /. Let x be a positive finiterepresentable number. List what each of the following evaluates to for eachoperation:(+?) ? xx ? (??)[Show the sign of your answer in each case.] [4 marks](c) Suppose the principles of IEEE arithmetic are applied to a floating-pointrepresentation with 6 bytes (48 stored bits). If ? = 2, emax = 511 and ahidden bit is used, deduce the values of emin and p. [4 marks](d) Define machine epsilon ?m. [1 mark](e) The functionf(x) = (x + 1)2×2 + 1is to be evaluated using IEEE arithmetic for x ? 0. Re-write the formulaso that f(x) can be evaluated in the case where x is representable but x2overflows. What does your formula evaluate to in the case that (1/x) < ?m?[4 marks]7 Computation Theory(a) Explain informally, i.e. without reference to any particular model ofcomputation, why the Halting Problem is undecidable. [6 marks](b) Briefly describe two mathematical problems, other than the Halting Problem,that are algorithmically undecidable. [4 marks](c) What does it mean for a partial function to be register machine computable?Show how the informal argument in part (a) can be turned into a rigorous proofthat there is no register machine deciding the Halting Problem for registermachine computable functions. [10 marks]5 [TURN OVERCST.2005.3.68 Computer Graphics and Image Processing(a) Calculate the maximum resolution needed by a movie projector in a movietheatre. Clearly state any assumptions that you make. [6 marks](b) Describe, in detail, an error diffusion algorithm for converting greyscale imagesto bi-level black and white images at the same resolution. [8 marks](c) Explain how this could be extended to provide an algorithm to print full colourRGB images on a CMYK laser printer, assuming that one pixel in the imagemaps to one pixel on the printer. [6 marks]9 Introduction to Security(a) A and B play a simple game. A chooses a number RA ? Z3 and B choosesa number RB ? Z3. Then A and B communicate their respective choice toeach other simultaneously, meaning that the players cannot change their choiceafter having seen that of the opponent. These rules decide who wins the game:RA ? RB + 1 (mod 3) ? A winsRB ? RA + 1 (mod 3) ? B winsIn any other case, the result of the game is a draw.(i) What complication arises when this game is played at a distance, forexample via e-mail? [2 marks](ii) Suggest a cryptographic protocol that prevents cheating when this gameis played via e-mail. Your solution should not rely on a trusted thirdparty. [6 marks](iii) What assumptions do you make about the cryptographic functions usedin your solution of part (ii)?To build a user-friendly tool for organizing your problem ideas. In particular, you want to build a form-based GUI program that will: (a) collect your ideas along with bits of evidence you can use to assess their worth; and (b) roughly rank the ideas based on their respective value. NOTE: There are going to be some basic requirements to the GUI, but the actual scene design is entirely up to you. The JavaFX module on Canvas provides a foundation on the basics of GUI building. Feel free to explore some other fun aspects of JavaFX! It is perfectly fine and essentially expected that you look up documentation on specific JavaFX classes. This homework is intentionally more open-ended, and we grade most of it manually. Before starting, make sure to install JavaFX. The instructions for that can be found on Canvas - Module 10.As part of your solution, you'll be provided two files FileUtil.java - A utility class to help with saving startup ideas into a file so that you can later view StartUpIdea.java - A class that represents a problem space to base your startup around. This class implements Comparable


