Fundamentals of Engineering (FE) Review Exam
Computers Software
Departamento de Ingenieria General
Recinto Universitario de Mayagüez
Universidad de Puerto Rico
Dr. Marco A. Arocha
10th August 2013
Content, Topics
Subjects o Numeric Systems & Conversions
o FORTRAN
o Flowchart Symbols
o Low-level Languages
o High-level Languages
o Assembly Language
o Pseudocode
o Logic Operations
o Spreadsheets
Content, FE Review
Glossary: In a separate document there is a selected
list of frequent used computer terms
Problems: Also a collection of FE like problems
Website: Some topics, problems, solutions, strategies,
and more. Under Construction
Numeric Systems Conversions
Binary Binary
Base-5 Base-5
Base-7 Base-7
Octal Octal
Decimal X X X Decimal
Hexadecimal X X Hexadecimal
Binary & Decimal • Decimal:
15610
• Binary:
100111002
• The binary system is the
internal language of
computers
• Computer programmers should understand how to
convert from decimal to
binary.
Binary Decimal
Bases Equivalent
0 0
1 1
2
3
4
5
6
7
8
9
Binary to Decimal 101110002 decimal
0 0X20
= 0
0 0X21
= 0
0 0X22= 0
1 1X23= 8
1 1X24
= 16
1 1X25
= 32
0 1X26
= 0
1 1X27128
sum 184
= 18410101110002
Hexadecimal & Decimal
Uses letters for the numbers from 10 to 15
Hexadecimal to Decimal 3B21AC16 decimal
C 12X160 = 12
A 10X161= 160
1 1X162= 256
2 2X163
= 8192
B 11X164
= 720896
3 3X165
= 3145728
sum = 3875244
= 3875244103B21AC16
High Level Languages Computer programs are written in specific languages:
“High-Level” and “Low-Level” Languages.
High-level programming language: o It is easy to use, resembles English
o Hide memory management
o Developing programs is simpler and more understandable relative to a
lower-level languages.
o The amount of abstraction provided defines how "high-level" a
programming language is.
o Examples of high-level programming languages include FORTRAN, C,
C++, VBA, FOCUS, Lisp, Perl, and Python.
FORTRAN In the past FE exam used FORTRAN as the high-level language of its choice. Still
sometimes you may found FORTRAN problems. The operators in FORTRAN:
Priority
FORTRAN sample question
What is the approximate value of variable S in the
FORTRAN statement shown?
S=(5.4)**(3.2)+5.4/2.5*1.5
(A)136
(B) 175
(C)224
(D)233
FORTRAN Hints 1. Square of 5: 5**2
2. Square root of 5: 5**0.5
3. - 3**2 = -(3**2) = -9, exponential operator has
higher priority than unary opertor “-”
4. A**B**C is equal to A**(B**C) rather than (A**B)**C
Low-Level Languages
Low-Level Languages: o MACHINE LANGUAGE
o ASSEMBLY LANGUAGE
Machine Language • instructions understood by
CPU
• made up of binary strings
of 0s and 1s
• instructions has two parts:
operation and operands
addresses
• instructions are a series of
bits
Assembly Language
• symbolic language
• Mnemonic codes for
operations
• Variables names
rather than addresses
• Uses macros (blocks of
codes than can be
repeated) referred by
names
• More sophisticated than machine
language
Assembly Language
For assembly language:
1. Assembly language code is translate into machine
language by an assembler
2. Functions libraries are combined by the linker
3. Program is placed into the computer memory by a
loader
Assembly Example Some times FE exam contains problems on basic
assembly
Data Movement Instruction
mov — The mov instruction copies the data item
referred to by its second operand into the location
referred to by its first operand
• Example:
mov eax, ebx — copy the value in ebx into eax
Assembly Example Arithmetic and Logic Instructions
• add — Integer Addition. The add instruction adds
together its two operands, storing the result in its first
operand.
• Example
add eax, 10 — means: EAX ← EAX + 10
Assembly Example Arithmetic and Logic Instructions
• sub — Integer Subtraction. The sub instruction stores
in the value of its first operand the result of
subtracting the value of its second operand from
the value of its first operand.
• Examples
sub al, ah — means: AL ← AL - AH
Assembly Example Arithmetic and Logic Instructions
• inc, dec — Increment, Decrement.
The inc instruction increments the contents of its
operand by one. The dec instruction decrements
the contents of its operand by one.
• Examples
dec eax — subtracts one from the contents of EAX.
inc eax— adds one from the contents of EAX.
Pseudocode • An informal language that helps programmers develop
algorithms
• A text-based detail algorithmic design tool.
• Each individual designer may have its own personal style of
pseudocode
• It has not a rigorous notation. There is no universal "standard."
• It is recommended that all statements showing "dependency" are to be indented. These include while, do, for, if, switch.
• In the FE exam this last advice is not follow.
• Examples below will illustrate this notion.
H = 1
J = 2
K = 3
L = 4
ANSWER = C
IF (H>J) OR (K<L) THEN ANSWER = A
IF (H<J) OR (K>L) THEN ANSWER = B
IF (H>J) OR (K>L) THEN H = 5
IF (H<J) AND (K<L) THEN ANSWER = D
Chose one:
A
B
C
D
Based on the following pseudocode, what is the
ANSWER?
Follow the value of the variables ANSWER and H after each IF:
IF (TRUE) ANSWER=A
IF (TRUE) ANSWER=B
IF (TRUE) H=5
IF (TRUE) ANSWER=D
Select (D) as the solution of the problem
Pseudocode Example
• How many times will the second line be executed?
M=42
LOOPSTART M=M-1
P=INTEGER PART OF (M/2)
IF P>15, THEN GO TO LOOPSTART
OTHERWISE GO TO END
END PRINT “DONE”
iteration M P P>15 GO TO
1 41 20 T LOOPSTART
2 40 20 T LOOPSTART
3 39 19 T LOOPSTART
4 38 19 T LOOPSTART
5 37 18 T LOOPSTART
6 36 18 T LOOPSTART
7 35 17 T LOOPSTART
8 34 17 T LOOPSTART
9 33 16 T LOOPSTART
10 32 16 T LOOPSTART
11 31 15 F END
Becareful: Most people will answer 10, however the 2nd
instuction M=M-1 will execute one more time to reach
the false condition 15>15 and then GO TO END
Pseudocode Example, Solution
Pseudocode Example
INPUT X
Y=0
Z=X+1
FOR K=1 TO Z
Y=Y+Z
NEXT K
Y=Y-(2*Z-1)
INPUT X
Y=0
Z=X+1
FOR K=1 TO Z
Y=Y+Z
NEXT K
Y=Y-(2*Z-1)
A program contains the following pseudocode
segment:
What is the final value of Y in terms of X?
(A) x2-1
(B) x2
(C) x2+1
(D) x2+2x+1
Pseudocode Example Solution
Alternative-1:
Within the loop Y is initialized to zero and then has Z
added to it Z times:
𝑌 =0+Z+Z+Z+Z+Z+Z+Z+..Z
Y=Z2 z added z times
After the loop
Y=Z2-2Z+1=(Z-1)2
Y=(X+1-1)2=X2
Pseudocode, Example Solution Alternative-2
Follow the pattern of the X and Y variable
X Z K Y, loop Y, final
0 1 1 1 0
1 2 1 2
2 0 1
2 3 1 3 Y=X2
2 6
3 9 4
3 4 1 4
2 8
3 12
4 16 9
Pseudocode Example
INPUT N, X
S=1
T=1
FOR K=1 TO N
T=(-1)*T*X^2/(2*K*(2*K-1))
S=S+T
NEXT K
What sum is calculated by the following
pseudocode program segment:
(A) 𝑆 = 1 −𝑥2
2 −
𝑥2
12 −
𝑥2
30 − ⋯ −
𝑥2
2𝑛(2𝑛−1)
(B) 𝑆 = 1 −𝑥2
2 −
𝑥4
12 −
𝑥6
30 − ⋯ −
𝑥2𝑛
2𝑛(2𝑛−1)
(C) 𝑆 = 1 −𝑥2
2! −
𝑥4
4! −
𝑥6
6! − ⋯ − (−1)𝑛 𝑥2𝑛
2𝑛 !
(D) 𝑆 = 1 −𝑥3
2! −
𝑥4
4! −
𝑥5
6! − ⋯ − (−1)𝑛𝑥𝑛+2
2𝑛 !
Pseudocode Example
Make a list for the values of S through the first few loops until
the pattern is evident
N=0 S=1
N= 1 𝑆 = 1 −𝑥2
2
N=2 𝑆 = 1 −𝑥2
2 −
𝑥4
24
N=3 𝑆 = 1 −𝑥2
2 −
𝑥4
24 −
𝑥6
720
N=n 𝑆 = 1 −𝑥2
2! −
𝑥4
4! −
𝑥6
6! − ⋯ − (−1)𝑛 𝑥2𝑛
2𝑛 !
ANSWER IS (C)
A flowchart is a step-by-step
drawing representing a specific
procedure or algorithm
www. allbusiness.com
Flowcharts
Flow Chart Symbols
Starts/Stops Decision [ decision must be made]
Input/Output [keyboard, printer, memory, permanent data storge]
Connector [point where several flow lines merge]
Processing [calculation]
Off-page [fc continues next page]
Predefined Process (library functions)
Annotation [comments]
Flowcharts
The terminal symbol starts or stops a process. The FE
problems typically involve a program fragment, so this
symbol might be used to distinguish a complete
program from a fragment
The decision symbol is a branch point in a flowchart. It
can only have one of two results, “true” or “false.” The decision symbol equate to an IF-ELSE statement, the
start of a WHILE loop, or the start of FOR loop.
The input/output symbol may be used in a program to
receive data from the user or to output data to the user or data storage.
Flowcharts
The processing symbol is where
mathematical (numerical or string)
operations take place
The connector symbol indicates where
several flow lines merge.
The off page symbol indicates that the
flowchart continues on the following page
Comments are placed on the annotation
symbol.
Which of the following flowcharts does not represent a complete program?
Flowcharts
The flowchart shown
represents the summer
training schedule for a
college athlete. What is the
regularly scheduled workout
on Wednesday morning?
(A) bike
(B) rest
(C) run
(D) weights
Flowcharts questions?
38
Logic Operations
Operators
AND
OR
NOT
39
‘AND’ True Table
Cond1 Operator Cond2 Result
T AND T T
T AND F
F AND T
F AND F
Expressions containing ‘AND’ are true only if both
conditions are true
40
‘OR’ True Table
Cond1 Operator Cond2 Result
F OR F F
T OR F
F OR T
T OR T
Statements containing ‘OR’ are false when both conditions
are false.
41
‘NOT’ True Table
NOT Cond Result
NOT T F
NOT F
‘NOT’ switches to false the expression if it is true and
viceverse.
42
Example • Let
A=5; B=3; C=6; D=8;
• Find the value of (A>B) AND (C>D)
(5>3 ) AND (6>8 )
T F
F
evaluate the terms
within the
parentheses first evaluate
43
Example • Let
A=5; B=3; C=6; D=8;
• Find the value of (A>B) OR (C>D)
(5>3) OR (6>8)
T F
T
evaluate
44
Example • Let
A=5; B=3; C=6; D=8;
• Find the value of ~( (A>B) AND (C>D))
~( (5>3) AND (6>8) )
T F
F
T
evaluate
FE Sample Problem • Given A= true, B= true, and C= false, what is the
value of the following expression?
• (A.AND.B).AND.(NOT.(C.OR.A))
(A)true
(B) false
(C)either true or false
(D)neither true nor false
FE Sample Problem Evaluate the terms within the parenthesis first, from the
inner to the outer parenthesis:
(A AND B) AND (NOT (C OR A))
(T AND T) AND (NOT (F OR T))
(T AND T) (NOT ( T )
(T AND F)
F
order
Spreadsheets A spreadsheet is a collection of items arranged in a tabular
format and organizaed in rows and columns. Typically, rows are
assigned numbers: 1, 2, 3, ... and columns are assigned letters: A,
B, C, ...
Cells
A cell is a unique element identified by an address consisting of
the column letter and the row number. For example, the address of the shaded cell above is D3. A cell may contain a number,
formula, or name.
Formulas Spreadsheets allow the construction of formulas in a
cell that may reference the content in other cells,
example:
The formula in the cell D3:
D3=C4+E5
Formulas When a cell containing a formula is copied to another cell, the
column and row references will automatically be changed by
others in the same relative position (this is called relative addressing)
Cell References
If D3=C4+E5 is copied to
C7=B8+D9
G6=F7+H8
Cell References If a row or column is referenced using absolute addressing (indicated
with a $ symbol) the row or the column reference will not changed
when a cell containing a formula is copied to another cell.
If C3 is copied to Result is
D3 D3=$B4+E$5+$A$1
C4 C4=$B5+D$5+$A$1
B4 B4=$B5+C$5+$A$1
E5 E5=$B6+F$5+$A$1
C3=$B4+D$5+$A$1
Spreadsheets
Computer programs consisting of tables of cells
containing values or formulas: • Cells are arranged in rows (labeled by numbers) and columns
(labeled by letters)
• Cells could be related to other cells
Example. The content of the cells in a spreadsheet are shown
What is the value of ‘T’ in the following program:
y=-3
z=y*3+10
T=D2-5*z
answer: T=-17
• How many cells are in the range C5...Z30
(A)575
(B) 598
(C)600
(D)624
Solution:
C5
Z35
From row 5 up to 30 there are 26 rows: 30-5+1=26
From column C up to Z there are 24 cols: 26-3+1=24
Total cells: 26x24=624, ANSWER IS (D)
Spreadsheets, sample problem
The cells in a spreadsheet are initialized as shown. The
formula B1+$A$1*A2 is entered into cell B2 and then
copied into B3 and B4. What value is displayed in B4?
• (A) 123
• (B) 147
• (C) 156
• (D) 173
The cells in a spreadsheet are initialized as shown. The
formula B1+$A$1*A2 is entered into cell B2 and then
copied into B3 and B4. What value is displayed in B4?
• (A) 123
• (B) 147
• (C) 156
• (D) 173 Need to compute each formula in
the order B2, B3, B4
Spreadsheets, sample problem
Referencias • Michael R. Lindeburg, 1999, “EIT Review Manual: Rapid Preparation for
the General Fundamentals of Engineering Exam”.
• Convert decimal to binary and viceversa: o http://www.wikihow.com/Convert-from-Decimal-to-Binary
o http://www.wikihow.com/Convert-from-Binary-to-Decimal
Good Luck !!!
