10 - April 2009 - Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering I Final Examination Thursday

1/6 ECSE 221 – April 23, 2009 Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering I Final Examination Thursday, April 23 rd , 2009 9:00am Examiner: Prof. F.P. Ferrie Associate Examiner: Prof. D.A. Lowther Instructions: Answer ALL 5 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) Assume that Intel introduces a new technology based on 3-state logic. How many distinct functions of two variables are possible using this scheme? [2 points] b) Using the same 3-state technology as in Part (a), Intel introduces a new computer with a 24-bit register size. What is the range of signed integers using this scheme? [2 points] c) Decode the IEEE 754 number 0x41500000 to its decimal equivalent. [2 points] d) Determine the minimal canonical forms corresponding to the following sum of products form: (4,6,7,10,11,14,15) A , B , C , D ∑ . [2 points] e) Implement the function in Part (d) with two 4-input multiplexers and one 2-input multiplexer. You may assume that complemented inputs are available. Draw the circuit diagram corresponding to your solution. [2 points] Question 2 a) Draw the circuit diagram corresponding to the first version of the SR latch described in the course notes (Module 2). Analytically derive the expressions corresponding to Q and Q for the NOR version of the latch and sketch the resulting circuit diagram. [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). You may assume that the circuit has been initially cleared to (Q1=0, Q0=0), and that A=1, B=0. Show 4 clock transitions from this initial state. [4 points]