05-Final - Department of Electrical Engineering McGill...

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1 Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering I Final Examination Friday, December 16 th , 2005 9:00 am Examiner: Prof. F.P. Ferrie Associate Examiner: Prof. D.A. Lowther Instructions: Answer ALL questions in the examination booklet provided, showing all of your work. Calculators are permitted, but they must be the Faculty standard. All questions are equally weighted. Question 1 a) A computer must sample an analog voltage in the range [-3.5v to 12.3v] to a precision of 0.5 mV. Assuming that the analog-to-digital converter used produces an output encoded as a 2’s complement integer, how many bits would be required? [2 points] b) Determine the range of decimal numbers that can be represented by a 5-digit, 8’s complement number. [2 points] c) Encode the number 2.62 x 10 17 using IEEE-754 single precision floating-point format. Express your answer as an 8-digit hexadecimal number. [2 points] d) Identify the function F A , B , C , D implemented by the multiplexer circuit shown below. [2 points] e) Determine the minimal canonical forms, ∑∏ and ∏∑ , corresponding to the following sum of products form: (2,3,5,7,11,13) A , B , C , D " . [2 points]
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2 Question 2 A finite state machine is implemented using a PROM and a 3-bit register as shown above. The timing parameters for this circuit are: T A (PROM) = 15 nS, T PD (D-FF) = 5 nS, T SU (D-FF) = 5 nS, and T H (D-FF) = 2 nS. The flip-flops are falling edge-triggered with identical parameters. a) Using the information provided above, determine the state transition table for this circuit and draw the corresponding state diagram. [2 points] b) From the state transition table, determine the next state equations for Q2, Q1 and Q0. [2 points] c) From the timing information provided, determine the maximum frequency of operation of the circuit (assuming the input is held constant) and plot the timing diagram corresponding to 3 state transitions, starting from [0,0,0] with the input set to 0. Make
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