1
Department of Electrical Engineering
McGill University
ECSE 221 Introduction to Computer Engineering I
Final Examination
Monday, December 6
th
, 2004
2:00pm
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 TV camera connected to a PC acquires a 640 x 480 pixel image 30 times per second.
Assuming that each pixel i) can represent one of 16 million colors, and ii) is represented
by an integer number of bytes, how much disk space is required to store 10 minutes of
video acquired by this camera?
[2 points]
b)
Determine the equivalent precision of the number 14B6.A31
16
in Base-3.
[2 points]
c)
An IEEE-like floating point representation is implemented on a computer with a 36-bit
register length.
Assuming that a 10-bit exponent is used, determine the range, precision,
and bias of this representation.
[2 points]
d)
Encode the number -1.52 x 10
30
using the floating point scheme described in Part (c).
(If
you are unsure of your answer, you may encode the number using IEEE-754, but with a 1
point penalty).
[4 points]
e)
Determine the minimal canonical forms corresponding to the following product of sums
form:
(1,3,4,5,6,7,8,9,12,14)
A
,
B
,
C
,
D
C
.
[2 points]
Question 2
a)
Analyze the circuit shown below and determine whether it corresponds to combinational
or sequential logic.
Express the output using the appropriate functional form (i.e.
Boolean function if combinational or next state equation if sequential).
[2 points]
4- i nput mul ti pl exer
D3
D2
D1
D0
S0
S1
Q
+5V
Y
X
Z