Visit http://www.swisswireless.org/wlan_calc_en.html

and go to the Antenna section. Observe  
the dynamics between the signal frequency, antenna diameter, and antenna gain of a parabolic
antenna.
1. Next to frequency band, select 2.41-2.48 GHz.
• Next to antenna diameter in meters, type 0.5 (0.5 meters = 19.7 inches). The most
common dish antenna ranges in size from 18 to 20 inches.
• Click D → dB. What is the maximum theoretical antenna gain of a common dish antenna at
the 2.4 GHz band? ___

• Next to frequency band, select 5.15-5.85 GHz.
• Next to antenna diameter in meters, type 0.5 (0.5 meters = 19.7 inches)
• Click D → dB. What is the maximum theoretical antenna gain of a common dish antenna at
the 5 GHz band? ___
Given the same-sized reflector, which signals, high-frequency, or low-frequency, can be more
efficiently focused by a common dish antenna (i.e., result in a higher antenna gain)? INCLUDE
YOUR ANSWERS in the Course Project PPT template for this module.

2. Next to frequency band, select 5.15-5.85 GHz.  

• Next to antenna diameter in meters, type 25 (25 meters = 82 feet). Each of the 27 antennas
of the very large array (VLA) radio telescope (one of the world's premier astronomical radio
observatories in New Mexico) is 25 meters in diameter. Note that this telescope operate at
a much higher frequency in real life.
• Click D → dB. What is the maximum theoretical antenna gain of the dish antenna used in
the VLA radio telescope in New Mexico at the 5 GHz band? ____
Given the same signal frequency, which dish antennas, large-sized or small-sized, are more
efficient at focusing the signal (i.e., result in a higher antenna gain)? INCLUDE YOUR ANSWERS
in the Course Project PPT template for this module.

1. What is the maximum theoretical antenna gain of a common dish antenna at the 2.4 GHz band? [4 points]

Answer:

2. What is the maximum theoretical antenna gain of a common dish antenna at the 5 GHz band? [4 points]

Answer:

3. Given the same sized reflector, which signals, high-frequency, or low-frequency, can be more efficiently focused by a common dish antenna (i.e., result in a higher antenna gain)? [5 points]

Answer:

4. What is the maximum theoretical antenna gain of the dish antenna used in the VLA radio telescopes in New Mexico at the 5 GHz band? [4 points]

Answer:

5. Given the same signal frequency, which dish antennas, large-sized or small-sized, are more efficient at focusing the signal (i.e., result in a higher antenna gain)? [5 points]

Free Space Path Loss

Visit http://www.swisswireless.org/wlan_calc_en.html and go to the Free space loss section. Observe the dynamics between the signal frequency, distance, and free space loss. 1. Next to the frequency band, select 2.41-2.48 GHz. ? Next to kilometers, type 0.1 (100 meters = 0.1 kilometers). ? Click dB ? km. What is the free space path loss in dB at the 2.4 GHz band? ___ ? Change the frequency band to 5.15-5.85 GHz. ? Next to kilometers, type 0.1 (100 meters = 0.1 kilometers). ? Click dB ? km. What is the free space path loss in dB at the 5 GHz band? ___

How does the free space path loss at a higher frequency (e.g., the 5 GHz band) compare with that at a lower frequency (e.g., the 2.4 GHz band)? INCLUDE YOUR ANSWERS in the Course Project PPT template for this module. 2. Next to the frequency band, select 2.41-2.48 GHz. ? Next to kilometers, type 0.02 (20 meters = 0.02 kilometers). ? Click dB ? km. What is the free space path loss in dB over 20 meters at the 2.4 GHz band? ___ ? Next to kilometers, type 0.04 (40 meters = 0.04 kilometers). ? Click dB ? km. What is the free space path loss in dB over 40 meters? ___ ? Next to kilometers, type 0.08 (80 meters = 0.08 kilometers). ? Click dB ? km. What is the free space path loss in dB over 80 meters? ___ When the distance doubles, how does free space path loss in dB change approximately? INCLUDE YOUR ANSWERS in the Course Project PPT template for this module. 3. The free space loss ??? can be expressed as ??? = 20log?+20 ????+?, where C is a constant that depends on the units of frequency (Hz, KHz, MHz, or GHz) and the distance from the antenna. The distance may be expressed in meters, Km, or miles. Moreover, for a given frequency and a fixed set of units of distance, we may express the free- space loss ??? as follows: ??? = 20log?+?, where K = 20 log f + C Therefore, the change in the free space loss (Delta ???) corresponding to a change from D1 to a larger distance D2 is Delta ??? = 20log?1?20log?2 , for any given frequency 4. Here are the basic operations of common logarithms (Log10(X) = Log(X) to the base 10). Zero Exponent Rule Log 1 = 0 (100 = 1) Product Rule Log (M*N) = Log M + Log N Quotient Rule Log (M/N) = Log M - Log N Power Rule LogMp = P*Log M Applying the quotient rule, the change in the free space loss (Delta ???) corresponding to a change from D1 to a larger distance D2 is expressed as: Delta ??? = 20log (?1/? 2) , for any given frequency

5. Use a scientific calculator to calculate Delta ??? for D1 = 20 meters and D2 = 40 meters. Delta ??? = _____ Is your calculation approximately the same as the result from Part 2 Step 2?

1. What is the free space path loss in dB at the 2.4 GHz band? [4 points] Answer:

2. What is the free space path loss in dB at the 5 GHz band? [4 points] Answer:

3. How does the free space path loss at a higher frequency (e.g., the 5 GHz band) compare with that at a lower frequency (e.g., the 2.4 GHz band)? [5 points]

Answer:

4. What is the free space path loss in dB over 20 meters at the 2.4 GHz band? [4 points]

Answer:

5. What is the free space path loss in dB over 40 meters at the 2.4 GHz band? [4 points]

Answer:

6. What is the free space path loss in dB over 80 meters at the 2.4 GHz band? [4 points]

Answer:

7. When the distance doubles, how does free space path loss in dB change approximately? [5 points]

Answer:

8. Use a scientific calculator to calculate Delta 33632496 for D1 = 20 meters and D2 = 40 meters. [4 points]

Delta 33632497= _____

9. Is your calculation approximately the same as the result from Part 1 Step 2? [4 points]

Answer: (a) For each of the following software project phases, suggest a design model or representation that would be a helpful aid in the design process. For each of these, sketch an example to show what this model looks like, based on some part of the above design brief. (i) Inception phase (ii) Elaboration phase (iii) Construction phase (iv) Transition phase [12 marks] (b) For each of the sketched examples in part (a), describe how the design work so far could be evaluated before proceeding to the next phase. [4 marks] (c) Choose two of the above design models, representations or evaluation methods, and explain how they would be done differently if the design project was following an agile rather than spiral project management approach. [4 marks] 7 (TURN OVER) CST.2014.2.8 SECTION D 7 Discrete Mathematics (a) Let m be a fixed positive integer. (i) For an integer c, let Kc = { k ? N | k ? c (mod m) }. Show that, for all c ? Z, the set Kc is non-empty. [2 marks] (ii) For an integer c, let ?c be the least element of Kc. Prove that for all a, b ? Z, a ? b (mod m) iff ?a = ?b. [4 marks] (b) (i) State Fermat's Little Theorem. [2 marks] (ii) Prove that for all natural numbers m and n, and for all prime numbers p, if m ? n

mod (p ? 1) then ? k ? N. km ? k n (mod p). [6 marks] (c) (i) Use Euclid's Algorithm to express the number 1 as an integer linear combination of the numbers 34 and 21. [3 marks] (ii) Find a solution x ? N to 34 x ? 3 (mod 21). [3 marks] any bugs that it may contain. Give more meaningful identifiers for the variables c and s. Give appropriate comments for the four positions marked "COMMENT HERE". Explain why the method returns a value and what the value means. [8 marks] 0 boolean delete(self, key) 1 # HEADER COMMENT HERE (1) 2 if self.u == 2: 3 if self.A[key] == 0 4 # COMMENT HERE (2) 5 return False 6 else: 7 c = self.cluster[high(key)].delete(low(key)) 8 if c: 9 # COMMENT HERE (3) 10 s = self.summary.delete(high(key)) 11 # COMMENT HERE (4) 12 return s 13 else: 14 return False 3 (TURN OVER) CST.2014.3.4 3 Programming in C and C++ (a) Write a C function revbits() which takes a single 8-bit char parameter and returns a char result by reversing the order of the bits in the char. [4 marks] (b) Write a C function revbytes() taking two parameters and returning no result. The first parameter is a pointer to memory containing n contiguous bytes (each of type char), and the second is the number of bytes. The function should have the side effect of reversing the order of the bits in the n contiguous bytes, seen as a bitstring of length 8n. For example, the first bit of the first char should be swapped with last bit of the last char. [6 marks] (c) You have been assigned the following seemingly working C code, which processes files controlling the behaviour of a system. You observe that, after obtaining several ERR_MALFORMED errors, subsequent calls to fopen fail due to too many files being open: int process_file(char *name) { FILE *p = fopen(name, "r"); if (p == NULL) return ERR_NOTFOUND; while (...) { ... if (...) return ERR_MALFORMED; process_one_option(); ... } fclose(p); return SUCCESS; } (i) Explain how to fix the program using facilities in C. [2 marks] (ii) Now suppose the function above was part of a system written in C++ (but still using the C file-processing commands such as fopen and fclose), and that process_one_option() might raise one or more exceptions. Using a class with a destructor, show how to fix the "too many files open" bug above. [8 marks] 4 CST.2014.3.5 4 Compiler Construction This question concerns the run-time call stack. (a) What is a run-time stack and why is it important to a compiler writer? [3 marks] (b) The implementation of a run-time call stack typically uses a stack pointer and a frame pointer. What are their roles and why do we need two pointers? [3 marks] (c) For some compilers the activation records (stack frames) contain static links. What problem are static links used to solve and how do they solve this problem? [3 marks] (d) (i) Consider a programming language that does not allow functions to be returned as results, but does allow the nesting of function declarations. Using ML-like syntax, we have the following code in this language. let fun f(x) = let fun h(k) = k * x fun g(z) = h(x + z + 1) in g(x + 1) end in f(17) end Draw a diagram illustrating the call stack from the call of f up to and including the call of function h. Make sure all function arguments are included in the diagram and clearly indicate static links. [5 marks] (ii) Using your diagram, explain how the code generated from the body of function h can access the values associated with the variables k and x. In each case make it clear what information is known at compile-time and what information is computed at run-time. [6 marks] 5 (TURN OVER) CST.2014.3.6 5 Compiler Construction Functional programmers will often rewrite a recursive function such as fun fact1 n = if n <= 1 then 1 else n * (fact1 (n -1)) to one such as fun fact2 n = let fun aux (m, a) = if m <= 1 then a else aux(m-1, m * a) in aux (n, 1) end using an accumulator (the parameter a of aux) and tail recursion. (a) Clearly explain the optimisation such programmers are expecting from the compiler and how that optimisation might improve performance. [4 marks] (b) The desired optimisation can be performed by a compiler either directly on the source program or on lower-level intermediate representations. Treating it as a source-to-source transformation, rewrite fact2 to ML code that has been transformed by this optimisation. You will probably use references and assignments as well as the construct while EXP do EXP. [8 marks] (c) Suppose that the programmer used instead a function as an accumulator. fun fact3 n = let fun aux (m, h) = if m <= 1 then h(1) else aux(m-1, fn r => m * (h r)) in aux (n, fn x => x) end Will your optimisation still work in this case? Explain your answer in detail. [8 marks] 6 CST.2014.3.7 6 Concepts in Programming Languages (a) Write a LISP program for detecting whether a LISP interpreter treats the language as being dynamically scoped (as was the case in historical LISP) or as being statically scoped (as is the case in modern LISP). You may use pseudo-code and should explain your answer in detail. [4 marks] (b) You manage two junior programmers and overhear the following conversation: A: "I don't know why anyone needs a language other than Java, it provides clean thread-based parallel programming." B: "Maybe, but I write my parallel programs in a functional programming language because they are then embarrassingly parallel." Discuss the correctness of these statements and the extent to which they cover the range of languages for parallel programming. [6 marks] (c) Explain why the SML interpreter accepts the declarations datatype 'a FBtree = node of 'a * 'a FBtree list; fun dfs P (t: 'a FBtree) = let exception Ok of 'a; fun auxdfs( node(n,F) ) = if P n then raise Ok n else foldl (fn(t,_) => auxdfs t) NONE F; in auxdfs t handle Ok n => SOME n end; while it does not accept the declaration exception Ok of 'a; [4 marks] (d) Consider the declarations structure Z = struct type t = int; val z = 0 end; structure A = Z : sig type t ; val z: t end; structure B = Z :> sig type t = int ; val z: t end; structure C = Z :> sig type t ; val z: t end; in the SML Modules language. Explain the behaviour of the SML interpreter on inputting each of the expressions Z.z = A.z; Z.z = B.z; Z.z = C.z; [6 marks] 7 (TURN OVER) CST.2014.3.8 7 Further Java Five housemates run a "status" server on their home network. The server stores the current status of each housemate as a string of text. For example, housemate Eva might set her status to "Gone to the exam hall." Messages are passed between clients and the server as text strings sent over TCP. The new line character is used exclusively as the last character in every message. On connection with the server, a client can either (i) query the status of a user by sending the user's name to the server as a string (and the server responds with the current status message), or (ii) set the status of a user by sending the user's name followed by a colon and the new status message. For example, "Eva:Gone to the exam hall." sets the status message for Eva. (a) Implement a status server in Java. The server should run indefinitely, responding to client requests. Once a client request has been fulfilled, the server should close the connection. You may assume current status messages are lost if the server is restarted and you do not need to handle exceptions. [8 marks] (b) One housemate suggests the server and client should communicate by serialising Java objects rather than sending messages as text. (i) Describe in words the changes you would make to your server implementation to send messages as serialised Java objects. [3 marks] (ii) List two advantages and two disadvantages of an implementation based on serialised Java objects versus sending messages as text. [4 marks] (c) Another housemate suggests that the server should not close the client's connection after answering the request. Instead the connection should remain open until the client sends another request or closes the connection. Describe in words what changes you would need to make to your implementation in part (a) to achieve this and comment on the advantages and disadvantages of this idea. [5 marks] 8 CST.2014.3.9 8 Prolog You are asked to write a Prolog program to work with binary trees. Your code should not rely on any library predicates and you should assume that the interpreter is running without occurs checking. 3 2 7 4 2 5 (a) Describe a data representation scheme for such trees in Prolog and demonstrate it by encoding the tree shown above. [3 marks] (b) Implement a Prolog predicate bfs/2 which effects a breadth-first traversal of a tree passed as the first argument and unifies the resulting list with its second argument. For example, when given the tree shown above as the first argument the predicate should unify the second argument with the list [3,2,7,4,2,5]. [4 marks] (c) Explain why the bfs/2 predicate might benefit from being converted to use difference lists. [2 marks] (d) Implement a new predicate diffbfs/2 which makes use of a difference list to exploit the benefit you identified in part (c). Your predicate should take the same arguments as bfs/2. [6 marks] (e) A friend observes that a clause in diffbfs/2 will need to contain an empty difference list and proposes two possible ways of representing it, either []-[] or A-A. Consider your implementation of diffbfs/2. For each use of an empty difference list, justify your choice and explain what can go wrong using the alternative form. [2 marks] (f ) Is your implementation amenable to last call optimisation (LCO)? If so, explain why. If not, give details of the minimal changes you would make to make LCO possible. [3 marks] 9 (TURN OVER) CST.2014.3.10 9 Software Engineering (a) Describe the main lessons learned from the report into the collapse of the London Ambulance Service. [12 marks] (b) To what extent have the developments in software tools and management practices of the last twenty years improved the situation, and which of the lessons do we still have to be careful of today?

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