# ECE2030D-E Introduction to Computer Engineering Fall 2003 Sample

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```					ECE2030D-E                           Introduction to Computer Engineering                          Fall 2003
Sample Midterm

I am providing this list of sample problems and their solutions to give you an idea of the type of problems
you COULD encounter on the mid-term. Please note that anything that we have covered in class during the
first half of the semester can show up on your mid-term. Typically I will give you 4-5 problems.

I will also provide a list of the Basic Boolean Identities.

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ECE2030D-E                         Introduction to Computer Engineering                   Fall 2003
Sample Midterm

Problem #1: (25 points) Binary Codes and Number Systems

a)   (5 points) How many bits do you need to have a binary code for 286 items?

28= 256 29=512 THEREFORE 9 bits are needed

a)   (5 points) Represent the fixed point base 10 number (82.25) 10 in base 2.

1010010.01

a)   (5 points) Represent the base 10 number (82.25)10 using binary coded decimal

(10000010.00100101)BCD

a)   (5 points) Represent the base 2 number (101001001001001111001)2 in hexadecimal

(149279)16

a)   (5 points) What is 0xAF230 in binary?

(1010 1111 0010 0011 0000)2

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ECE2030D-E                        Introduction to Computer Engineering                            Fall 2003
Sample Midterm

Problem 2: (25 points) Boolean Algebra

a)   (15 points) Derive the simplified SOP of the following expression using Boolean algebra. Please

F = x1 x 2 x 3 + x1 x 2 x 3 + x1 x 3 x 4 + x 4 x1 + x1 x1
= x1 x 2 x 3 + x1 x 2 x 3 + x1 x 3 x 4 + x 4 x1 + 0
= x1 x 2 (x 3 + x 3 ) + x1 x 3 x 4 + x 4 x1
= x1 x 2 + x1 (x 3 x 4 + x 4 )
= x1 x 2 + x1 (x 3 + x 4 )
= x1 x 2 + x1 x 3 + x1 x 4
a)   (10 points) Apply DeMorgan’s Theorem to the following expression to simplify into SOP form.

†
F = x1 x 2 x 3 x 4 + x 5

= (x1 x 2 x 3 x 4 )x 5
= (x1 x 2 x 3 + x 4 )x 5
= ((x1 + x 2 )x 3 + x 4 ) x 5
= x1 x 3 x 5 + x 2 x 3 x 5 + x 4 x 5

†

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ECE2030D-E                      Introduction to Computer Engineering                         Fall 2003
Sample Midterm

Problem #3: (25 points) CMOS circuit Design

a)   (10 points) Design the complex CMOS circuit to implement the following function.
Assume that you have the complemented and un-complemented version of the input
variables at your disposal. BE SURE YOU LABEL THE OUTPUT OF CIRCUIT.

F = x1 x 2 + x 3

†           Vdd                              Logic “1”

X1                      X2

X3
F

X1
X3

X2

GRD            Logic “0”

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ECE2030D-E                     Introduction to Computer Engineering                       Fall 2003
Sample Midterm

b) (10 points) Given the following nFET network, please draw the corresponding pFET network.
Once completed, draw a line through network to show the conducting path through this
network for x1 = LOW, x2=LOW, x3=HIGH, x4=LOW. Is the output high or low?

Vdd

X1               X2

X3               X4

x1                                         x3

x2                                          x4

GRD

b) (5 points) What does the acronym MOSFET stand for?

Metal Oxide Semiconductor Field Effect Transistor

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ECE2030D-E                         Introduction to Computer Engineering                             Fall 2003
Sample Midterm

Problem 4: (25points) Gate Design Methodology

(a) (10 points) Consider the following schematic that is provided with no information other than that
the designer used mixed logic notation. Write down the original Boolean function that the designer
used to make this logic schematic.

F = X + Y + Z + ABC

Y
†   X
Z

A
B                                                                            F
C

(b) (10 points) Implement the following function using OR gates only. Be sure you use mixed logic
notation. Assume that you only have the un-complemented form of the signals available to you. BE
SURE THAT YOU DO NOT TRY TO ALTER F WITH BOOLEAN ALGEBRA. After you finish
your circuit be sure you indicate how many transistors you need.

F = x1 x 2 + x 3
# Transistors = 20

2           6
X1           †                                   6
2
X2
2

X3
2

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ECE2030D-E                       Introduction to Computer Engineering                            Fall 2003
Sample Midterm

c) (5 points) Show the most efficient transistor level CMOS circuit implementation of an OR function.
Assume that you have available to you the un-complemented signals X and Y (i.e. if you need the
complement you must show that)

4        2
NOR GATE
Vdd
Inverter

X                                                                                     Vdd

Y
X+Y

X                    Y
GRD

GRD

7/9
ECE2030D-E                           Introduction to Computer Engineering                  Fall 2003
Sample Midterm

Problem #5 (20points) –Building Blocks

Fill in the truth table that describes the output of the following circuit.
Z
4-to-1 MUX

0
1
2                                  output
3
+                                                          S1 S0
Vdd
-
GRD
Y     X

Y                  X                           Z             output

0                  0                   0                     1

0                  0                   1                     0

0                  1                   0                     0

0                  1                   1                     1

1                  0                   0                     0

1                  0                   1                     0

1                  1                   0                     1

1                  1                   1                     1

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ECE2030D-E                        Introduction to Computer Engineering                             Fall 2003
Sample Midterm

Problem #6 (20points) – Number Systems

(a) (5 points) The following number is a 5-bit signed number that uses 2’s complement to represent
negative numbers. Give the decimal equivalent.

(10010)2 = (?)10

1) We know it is negative because MSB is 1
2) To get the positive magnitude take the 2’s complement (i.e. flip the bits and add 1)

01101
+   1                                           -14
01110 -----> 14

(b) (5 points) Using the same 5-bits in part (a) NOW assume that the number is a signed number that
uses signed-magnitude representation of negative numbers. Give the decimal equivalent.

(10010)2= (?)10

1) We know that it is negative because the MSB is 1
2) With signed magnitude, we can read the other bits as a postive number

0010 ---- > 2
-2

9/9

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