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2 - April 2004 [Karna Hai]

# 2 - April 2004 [Karna Hai] - Department of Electrical...

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1 Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering I Final Examination Friday, April 30 th , 2004 2:00pm Examiner: Prof. F.P. Ferrie Associate Examiner: Prof. T. Arbel 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 graphics card for a PC can display an image with a maximum resolution of 1280 x 1024 pixels with 24 million color possibilities for each pixel. How much memory does this graphics card require to operate at this maximum resolution? Express your answer in bytes. [2 points] b) An IEEE-like floating representation is to be designed for a computer with a 48-bit register size. Determine the smallest mantissa field size capable of supporting 11 decimal digits of precision. [2 points] c) Using the result you obtained in Part b, encode the number 3.51x10 -16 using this 48-bit floating point scheme. (If you are unsure of your answer, you may encode the number using IEEE-754, but with a 1 point penalty). [4 points] d) Determine the minimal canonical forms corresponding to the following sum of products form: (2,3,4,6,8,12,14) A , B , C , D . [2 points] Question 2 a) A single-bit full adder produces outputs i and c i+1 from inputs a i , b i , and c i . Show how this device can be implemented using two 4-input multiplexers and a single inverter. [2 points] b) Produce the next state equations, state transition table, and timing diagram for the circuit shown at the top of the next page (you may ignore delays).

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