2 ECAD Consider the following mysterious Verilog module. [15 marks] Give and explain two examples of theorems about the behaviour of Standard ML programs which can be expressed and proved in terms of either or both of the two logical systems described above. Show how to encode a general register machine program and the initial configuration of one of its computations into a pair of natural numbers. [6 marks] Outline the design of a register machine that simulates a general register machine computation specified by a single natural number [4 marks] (d) Which of the lookup mechanisms in part (b) is usually used for a TLB and why aren't the other mechanisms usually used? It may be assumed that n > 1. [5 marks]

A hardware device generates streams of ternary digits. Within a stream, each digit

is equiprobably 0, 1 or 2. A stream ends as soon as each digit has been seen at least

once.

(d) What is the probability that the first k digits comprise exactly two of the three

available digits? [1 mark]

(e) For r > 2, what is the probability that a stream is r digits long? [3 marks]

(f ) What is the expected length of a stream? [5 marks]

Hint: It may be useful to note that

X

r=1

rxr1 =

1

(1 x)

2

if 0 6 x < 1

4

CST.2001.2.5

5 Probability

Candidates for a certain first-year University Examination offer four subjects. b) Describe the purpose and four typical functions of a root kit. [6 marks] 9 (TURN OVER) CST.2014.4.10 9 Security I Block ciphers usually process 64 or 128-bit blocks at a time. To illustrate how their modes of operation work, we can use instead a pseudo-random permutation that operates on the 26 letters of the English alphabet: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 m A B C D E F G H I J K L M N O P Q R S T U V W X Y Z EK(m) P K X C Y W R S E J U D G O Z A T N M V F H L I B Q As the XOR operation is not defined on the set {A, . . . , Z}, we replace it here during encryption with modulo-26 addition (e.g., C D = F and Y C = A). (a) Encrypt the plaintext "TRIPOS" using: (i) electronic codebook mode; [2 marks] (ii) cipher-block chaining. Give and explain two examples of theorems about the behaviour of Standard ML programs which can be expressed and proved in terms of either or both of the two logical systems described above. Show how to encode a general register machine program and the initial configuration of one of its computations into a pair of natural numbers. [6 marks] Outline the design of a register machine that simulates a general register machine computation specified by a single natural number. Your machine should take appropriate action for all possible inputs. [6 marks] 6 In what ways does the assumption of spatial locality of reference influence the design of the virtual memory system? .Explain how their self-Fourier property and their closure under multiplication (i.e. the product of any two of them is yet again a Gabor wavelet) gives them also closure under convolution. Mention one disadvantage of such wavelets for reconstructing data from their projection coefficients.and explain what is meant by a relational schema. [4 marks] (iii) Explain how a formal schema can assist both the application database designer and a database application programmer. What if any are the disadvantages of adopting a mathematical description of database structure? [5 marks]