Chapter 2
Data Representation in
Computer Systems
Lecture Overview
Positional Numbering System
Decimal to binary conversion
Signed integer representation
Floating-point representation
Prepared by Dr. Hassan SALTI - 2012
2
Positional Numbering System
Posit
Revision for the MTA
Try to solve all exercises related to chapters:
1,2,3
Review Questions
Which of the following is not a CPU component?
a- A main memory.
b- A program counter.
c- A control unit.
d- An arithmetic logic unit.
Which of the following stora
Linear Transformation, Null
Spaces and Ranges
Linear Transformations
Definition:
Let V and W be vector spaces. The mapping
T :V W
is called linear transformation if for every X , Y in V
and c in R ,
T ( X Y ) T ( X ) T (Y )
T (cX ) cT ( X )
x y
e.g. T
Arab Open University
Faculty of Computer Studies
M132: Linear Algebra
Linear Algebra
When you take a digital photo with your
phone or transform the image in
Photoshop, when you play a video game or
watch a movie with digital effects, when
you do a web sea
Matrices and Matrix Operations
Matrices
An mn matrix A is a rectangular array of mn real numbers
arranged in m horizontal rows and n vertical columns. The matrix
A has size mn. The element in the row i and column j of the
matrix A is written as aij .
Exam
Vector Spaces, Subspaces,
Span, Bases and Dimensions
Vector Spaces
Definition:
A real vector space is a set of elements V together w ith two operations and
satisfying the following properties :
For every U , V , W in V,
U V in V
U V V U
(U V ) W U (
Determinant of a Matrix
Determinant of a Matrix
Determinant of a 22 matrix:
a b
The determinan t of the matrix A
, denoted by A or det( A),
c d
a b
is given by A det( A)
ad bc.
c d
3 4
3 4
e.g. If A
, then A
(3)(2) (4)( 1) 10.
1 2
1 2
Determinant
Vectors, Linear Combinations
and Linear Independence
Vectors in Rn
Vectors in Rn:
v1
v
An n - vector V 2 is called a vector in R n , where v1 , v2 , , vn R
vn
are called the components of the vector.
2
e.g. X is a 2 - vector, vector in R 2 or ve
Eigenvalues and Eigenvectors
of a Matrix
Eigenvalues and Eigenvectors
Definition:
Let A be an n n matrix. A number is called an eigenvalue
of A if there exists a nonzero vector X such that AX X .
Every vect or X satisfying the above equation is called an
M105 Meeting 1 - Extra Exercises
Notes:
1) You need to install JDK + IDE in your machine (or use an online compiler) in order to
solve the below exercises. The file "How to install JDK and IDE" could help you.
2) You could access the website of the text b
M105 Meeting 1 - Exercises
Exercise 1:
Write, compile and execute the Java program in Figure 2.1 in the text book.
Exercise 2:
Modify your program in Q1 to be as in Figure 2.3 in the text book.
What happened when you tried to edit the class name? How coul