4 - April 2005 [WEBCT] [Done]

# 4 - April 2005 [WEBCT] [Done] - Department of Electrical...

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1 Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering I Final Examination Thursday, April 21 st , 2005 2:00pm Examiner: Prof. F.P. Ferrie Associate Examiner: Prof. J. Clark 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) The IEEE double precision format has a 52-bit mantissa. Determine the precision and range of real numbers that can be represented using this format. [2 points] b) Divide 10100111 2 by 111 2 using binary long division. [2 points] c) Encode the number –1.42 x 10 -19 using IEEE-754 single precision floating-point format. Express your answer an 8-digit hexadecimal number. [2 points] d) Prove that the contents of two binary variables, A and B, can be exchanged by the following sequence of operations: A=XOR(A,B) B=XOR(A,B) A=XOR(A,B) [2 points] e) Determine the minimal canonical forms corresponding to the following sum of products form: (5,8,9,10,12,13,14) A , B , C , D [2 points] Question 2 J C K S R Q Q J C K S R Q Q J C K S R Q Q +5V +5V +5V +5V Clr Clk Mode Q2 Q1 Q0

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2 The circuit shown on the previous page is comprised of rising edge-triggered J-K flip-flops and combinational logic. At T=0, it is initialized to <Q2=0, Q1=0, Q0=0> by applying a reset pulse to the asynchronous Clr input. Under normal operation, the circuit will count in one of two sequences depending on whether the Mode input is 1 or 0. Answer the following questions: a) Determine the next state equations corresponding to Q2, Q1, and Q0 respectively. Use these equations to then determine the state transition table corresponding to this circuit. [3 points] b) Assume that each gate has Tpd=0.1nS and that gates with inverted inputs (indicated by a bubble on the inverted input) have Tpd=0.15nS. The timing parameters for flip-flops Q2 and Q0 are identical, Tpd=1nS, Th=0.1nS, and Tsu=0.25nS. Flip-flop Q1 has Tpd=1.5nS, Th=0nS, and Tsu=0.4nS. Determine the maximum frequency of operation for this circuit. Next, produce a detailed timing diagram showing three clock transitions beginning with <Q2=0, Q1=0, Q0=0> and Mode=0. [3 points] c) Show how this circuit can be re-implemented with a read-only memory (ROM) and 3 D
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4 - April 2005 [WEBCT] [Done] - Department of Electrical...

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