By what principle can you claim that each of your proposed questions in the sequence is maximally informative? To what value should the Examiners lower the threshold mark for a First

overall to ensure that approximately one-third of the candidates gain Firsts?

[5 marks]

(c) What is the probability that a candidate obtains or exceeds this lower

threshold? [1 mark] The maximum memory read bandwidth is 100 GB/s. (i) What is the effective memory access latency? [4 marks] (ii) A colleague suggests replacing the system above with one that provides 80 GB/s memory read bandwidth and main memory access latency of 30 ns. Explain whether you should accept the replacement or not, and why. [4 marks] (c) A creative engineer suggests structuring the TLB so that not all the bits of the presented address need match to result in a hit. Suggest how this might be achieved, and what might be the costs and benefits of doing so. [6 marks]

(a) Describe two quantitative and two qualitative techniques for analysing the usability of a software product. [4 marks] (b) Compare the costs and benefits of the quantitative techniques. [6 marks] (c) Compare the costs and benefits of the qualitative techniques. [6 marks] (d) If restricted to a single one of these techniques when designing a new online banking system, which would you choose and why?

(a) Suppose that women who live beyond the age of 80 outnumber men in the same age group by three to one. How much information, in bits, is gained by learning that a person who lives beyond 80 is male? [2 marks] (b) Consider n discrete random variables, named X1, X2, . . . , Xn, of which Xi has entropy H(Xi), the largest being H(XL). What is the upper bound on the joint entropy H(X1, X2, . . . , Xn) of all these random variables, and under what condition will this upper bound be reached? What is the lower bound on the joint entropy H(X1, X2, . . . , Xn)? [3 marks] (c) If discrete symbols from an alphabet S having entropy H(S) are encoded into blocks of length n symbols, we derive a new alphabet of symbol blocks S n . If the occurrence of symbols is independent, then what is the entropy H(S n ) of this new alphabet of symbol blocks? [2 marks] (d) Consider an asymmetric communication channel whose input source is the binary alphabet X = {0, 1} with probabilities {0.5, 0.5} and whose outputs Y are also this binary alphabet {0, 1}, but with asymmetric error probabilities. Thus an input 0 is flipped with probability , but an input 1 is flipped with probability , giving this channel matrix p (i) Give the probabilities of both outputs, p(Y = 0) and p(Y = 1). [2 marks] (ii) Give all the values of (, ) that would maximise the capacity of this channel, and state what that capacity then would be. [3 marks] (iii) Give all the values of (, ) that would minimise the capacity of this channel, and state what that capacity then would be. [3 marks] (e) In order for a variable length code having N codewords with bit lengths 1 mark] (f ) The information in continuous signals which are strictly bandlimited (lowpass or bandpass) is quantised, in that such continuous signals can be completely represented by a finite set of discrete samples. Describe two theorems about how discrete samples suffice for exact reconstruction of continuous bandlimited signals, even at all the points between the sampled values. [4 mark

(a) A two state Markov process emits the letters {A, B, C, D, E} with the probabilities shown for each state. Changes of state can occur when some of the symbols are generated, as indicated by the arrows. 4.2 Information sources with memory We will wish to consider sources with memory, so we also consider Markov processes. Our four event process (a symbol is generated on each edge) is shown graphically together with a two state Markov process for the alphabet fA, B, C, D, Eg in gure 17. We can then solve for the state occupancy using ow equations (this example is trivial).