What is the critical path of a synchronous clock domain and how does it affect performance? [2 marks] (b) Name two tools that can be used for locating the critical paths of a system on chip before fabrication. Which is faster or better and why? [4 marks] (c) Explain how pipelining can alter performance. What are its disadvantages? [4 marks] (d) How does pipelining alter the state encoding for a sub-system? [2 marks] (e) Name a tool that can be used to formally check whether a minor design change has altered the behaviour of a subsystem where the state encoding has not been changed. Name another tool for use when the state encoding may have been changed. [2 marks] (f ) Using any combination of diagrams, SystemC or RTL, sketch two implementations for a design of your choosing that use a different number of flip-flops to achieve the same functionality. Explain whether the reports from each of your two tools from part (e) might differ for your two implementations. [6 marks]

Consider the following grammar: ce, cats} V ? {saw, grinned} (a) The grammar can be used to generate the following sentences: (i) Alice saw cats (ii) Cats Alice saw grinned Draw derivation trees for both of these sentences. [2 marks] (b) What is the longest sentence that can be generated by the grammar? Describe this sentence. [2 marks] (c) Is the language generated by the grammar a regular language? Provide a proof for your answer. [8 marks] (d) A psycho-linguistic experiment shows that, by the 2nd word in the sentence, Part (a)(ii) is harder to process than the sentence Part (a)(i). Yngve hypothesised that a speaker's short-term memory functions as a stack. Explain how this hypothesis might account for the experimental results by drawing the stack arising from a top-down parse of the two sentences. [4 marks] (e) How might the sentence in Part (a)(ii) be altered so that it has the same meaning but is easier to process? Explain your reasoning.

A Boolean satisfiability problem has four variab? x3) ? (x2 ? x3) ? (x1 ? x2 ? x4). (1) The aim is to find assignments to the variables such that f is true under the usual rules for Boolean operations. This question addresses the use of more general constraint satisfaction to solve this problem. (a) Give a general description of a constraint satisfaction problem (CSP). [3 marks] (b) Explain how a Boolean satisfiability problem in CNF form and with n variables can be converted to a CSP, also having n variables and having a suitable constraint for each clause. Illustrate your answer using the 4-variable formula f in (1). [3 marks] (c) Explain, again using a constraint corresponding to a clause from (1), how general constraints can be converted to binary constraints. Provide a graph illustrating the problem from (1) after it has been converted to a CSP with only binary constraints. [4 marks] (d) Explain, how forward checking works in the context of a general CSP. How does this benefit a CSP solver? [3 marks] (e) Using the CSP equivalent you developed for (1), with only binary constraints, demonstrate how forward checking works using the sequence of assignments x1 = F, x2 = F, x4 = T. [5 marks] (f ) How would you expect the solution obtained when applying forward checking to be affected if constraints were allowed to propagate more widely? [2 marks]

A program is required to draw an arc from (0, 1) to (1, 0) of the circle centred t the origin with unit radius. (a) One approach would be to draw a segment of the cubic Overhauser curve defined by (?1, 0), (0, 1), (1, 0) and (0, ?1). (i) Explain how a segment of an Overhauser curve in general can be represented as an Hermite cubic and so as a Bezier cubic. [4 marks] (ii) Derive the formula for the resulting Bezier curve, P(t). [3 marks] (iii) Calculate the coordinates of P( 1 2 ). How large is the error? [Hint: ? 2 ? 1.414.] [3 marks] (b) Calculate revised control points for the Bezier curve so that it models the circular arc more accurately. [4 marks] (c) Describe in outline an alternative way of efficiently drawing the arc by calculating the pixels that lie on it directly.

(a) State what is meant by a directed graph and a strongly connected component.

Illustrate your description by giving an example of such a graph with 8 vertices

and 12 edges that has three strongly connected components. [5 marks]

(b) Describe, in detail, an algorithm to perform a depth-fifirst search over such a

graph. Your algorithm should attach the discovery and fifinishing times to each

vertex and leave a representation of the depth-fifirst spanning tree embedded

within the graph. [5 marks]

(c) Describe an O(n) algorithm to discover all the strongly connected components

of a given directed graph and explain why it is correct. You may fifind it useful

to use the concept of the forefather ?(v) of a vertex v which is the vertex, u,

with highest fifinishing time for which there exists a (possibly zero length) path

from v to u. [10 marks]

2 Computer Design

(a) What is a data cache and what properties of data access does it exploit?

[5 marks]

(b) What is a direct mapped cache and under what conditions will it exhibit poor

performance? [5 marks]

(c) Under what circumstances might a word of data in main memory be

simultaneously held in two separate fifirst-level cache lines? [5 marks]

(d) A translation look aside buffffer is a specialised cache. What does it typically

store and why is it often a factor of 1000 smaller than a data cache? [5 marks]

2CST.2001.6.3

3 Digital Communication I

(a) Defifine the terms circuit and packet in the context of communication systems.

[5 marks]

(b) What sort of guarantee does circuit switching provide? [5 marks]

(c) What advantages does packet switching provide over circuit switching?

[5 marks]

(d) Which of frequency division multiplexing, time division multiplexing and code

division multiplexing lend themselves to circuit switching? Which to packet

switching? Explain why or why not in each case. [5 marks]

4 Computer Graphics and Image Processing

(a) Describe the z-buffffer polygon scan conversion algorithm. [10 marks]

(b) In ray tracing, once we have determined where a ray strikes an object, the

illumination at the intersection point can be calculated using the formula:

Explain what real effffect each of the three terms is trying to model and explain

what each of the following symbols means, within the context of this formula:

I, Ia, i, Ii , ka, kd, ks,Li, N, Ri, V, n

Transcribed Image Text:

10. (10pts) Recall the attributed grammar from question 8. Consider the following de- notational semantics: densem( ENDLINE ) = densem( ) U densem( ) densem (ID "->" ) = {(ID, bodysem( ))} bodysem( "," ) = bodysem( ) + bodysem( ) body sem (ID) if ID = main then 10 else 1 bodysem("&") = 2 bodysem("") = 100 bodysem("*") = -10 NOTE: The format is similar to our example from class. The semantics in this ques- tions is different from the one presented in other questions. For the following programs, what is the mathematical meaning? Briefly explain why. (a) main > step, show step -> &, & show > %,&,* (b) main -> one, two, three, four one -> two, &,* two -> &, & three > four,*,& four -> *,*,&,% 10. (10pts) Recall the attributed grammar from question 8. Consider the following de- notational semantics: densem( ENDLINE ) = densem( ) U densem( ) densem (ID "->" ) = {(ID, bodysem( ))} bodysem( "," ) = bodysem( ) + bodysem( ) body sem (ID) if ID = main then 10 else 1 bodysem("&") = 2 bodysem("") = 100 bodysem("*") = -10 NOTE: The format is similar to our example from class. The semantics in this ques- tions is different from the one presented in other questions. For the following programs, what is the mathematical meaning? Briefly explain why. (a) main > step, show step -> &, & show > %,&,* (b) main -> one, two, three, four one -> two, &,* two -> &, & three > four,*,& four -> *,*,&,%