Numerade

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Question 2. Consider a floating-point system that expresses numbers in the form $\sigma \times a \times 2^e$, where $\sigma = \pm 1$, $1 \le a < 2$ and $-1022 \le e \le 1023$. This system uses 10 bits for the fractional part of the significand $a$ (that is, $a$ has the form $1.a_1a_2...a_{10}$ where each $a_i \in \{0, 1\}$). Determine the representation for the following decimal numbers in this floating-point system: 1. 5.6, using round up. 2. 5.6, using round to nearest. 3. -5.6, using round towards 0. 4. -5.6, using round down.

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B. Consider the following UML class diagram. Employee - id: int - salary: double Employee(id: int, sal: double) Employee(id: int) +setSalary(sal: float) +getID(): int +getSalary(): double Programmer - bonus: int Programmer(id: int, salary: double, bonus: int) Programmer(id: int) +setBonus(bonus: int) +getBonus(): int +getSalary(): double i. Write the Java code to implement the Programmer class.

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When a fund has to sell illiquid assets quickly to raise cash to meet investors' withdrawal requests, a fire sale has occurred.

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Lambda terms as discussed in the class are defined by the following grammar: t ::= x | (?x.t) | (tt) evaluation rule (called ? rule) is defined as follows (?x.t) r ?? t [x ? r] Bellow is given types for lambda terms: type 'a lambda = Var of 'a | Fun of 'a * 'a lambda | App of 'a lambda * 'a lambda Implement the beta rule of lambda calculus. Hint: In the implementation you have to take care variable renaming to avoid variable capture (No free variable should get bound after reduction!) For example: (?x.xx) y reduces with the ? rule to yy (?x.?y.x) y z reduces with the ? rule to (?y.y) z and not (?y.y)z If you implement outermost strategy (lazy evaluation) a term (?x.(?y.xy)z)l reduces by the ? rule to (?y.ly)z. If you implement innermost strategy (eager evaluation) the same term (?x.(?y.xy)z)l reduces to (?x.xz)l

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Simplify the expression. Write the result using positive exponents only. Assume t = (-20m^4n^-5)/(5m^-2n^-2)

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4. Addition of velocities: a. Show that a galilean boost in the $x$ direction with velocity $v_1$, followed by another in the same direction with velocity $v_2$, is the same as a single such boost with velocity $v_1 + v_2$. b. Show that a Lorentz boost in the $x$ direction with velocity $v_1$, followed by another in the same direction with velocity $v_2$, is the same as a single such boost with velocity $\frac{v_1 + v_2}{1 + v_1v_2}$. (23) Note that this never exceeds the speed of light as long as $v_1$ and $v_2$ don't.

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Problem 13.2-32 (Companion Problem) Your answer is incorrect. Try again. 40 µF=\\ R? is(t) R?\\ 10(t) The input to this circuit is the current of the current source, $i_s(t)$. The output is the current, $i_o(t)$, in resistor $R_2$. The network function that represents this circuit is Determine the values of the resistances in this circuit. $R_1 =$ 0.001818 ? and $R_2 =$ -0.0008748 ?. $H(\omega) = \frac{I_o(\omega)}{I_s(\omega)} = \frac{1 + j\frac{\omega}{4545}}{1 + j\frac{\omega}{2258}}$

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Please answer the following questions: Question 1: (10 Marks) One digital communication system for error control coding use the convolutional encoder and Viterbi decoding. The structure of the convolutional encoder realized in the controller canonical form (CCF) is shown in Figure 1 a) Find the transform-domain generator matrix $G(x)$ b) Find the time-domain generator matrix c) Find the code rate and draw the state diagram. Is the encoder a systematic one? 1 Mark 2 Marks 3 Marks

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QUESTION 4 (a) Discuss the conditions for contestable markets. Show (using a game tree) how government intervention may be unnecessary to achieve average-cost pricing in the absence of the inertia shopping rule. (4 marks) (b) Using a carefully labelled diagram, explain how the equilibrium wage is determined when the labour market is characterised by a bilateral monopoly. (4 marks) (c) In a Prisoner's Dilemma, if the game is repeated for many periods, identify four (4) factors that can lead to a cooperative outcome. (2 marks) [Total for Question 4: 10 marks]

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The so-called participation problem with Plato's theory of the Forms arises from an attempt to overcome the so-called Third Man problem. True/False? 2. According to class discussion, both Aristotle and Aquinas believe that God necessarily has knowledge of things in the natural world. True/False? 3. According to class discussion, St. Thomas Aquinas maintains that God's existence can only be known by faith and not proven by reason. True/False?

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