Introduction to computer science Fall-2018

1. +
Dr Ramadan Babers
Faculty of Science - Helwan University
Fall – 2018
Introduction
to
Computer
LEC - 2

2. +
Data Representation
2

3. Chapter 2 Outlines
 Introduction
 Numbering Systems
 Binary Logic
 Representing Characters
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4. 2.1 Introduction
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 Computer systems operate using two voltage
levels (usually 0 volt and +5 volt).
 With two such levels, we can represent exactly two
different values, zero and one.
 All kinds of information processed by the computer
are expressed using only these two values.

5. 2.2 Numbering Systems
2.2.1 Overview of the Decimal Numbering System
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 We use the decimal system, also called base 10, because
we have ten fingers.
 In decimal, a numeric quantity is represented by a series of
digits from 0 to 9.

6. 2.2 Numbering Systems
2.2.2 The Binary Numbering System
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 The binary numbering system is a base 2 numbering
system.
 A “binary digit” is called a bit.

7. 2.2 Numbering Systems
2.2.2 The Binary Numbering System
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 Four bits can represent 16 different values.
 If we use them to represent unsigned integers, we
obtain the range 0 (0000) to 15 (1111).
 In general, n bits can represent the 2n unsigned
integers 0 to 2n-1.
 For example 8 bits (one byte) can represent the
numbers from 0 (00000000) to 255 (11111111).

8. 2.2 Numbering Systems
2.2.2 The Binary Numbering System
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2.2.2.1 Conversions between Binary and Decimal Systems
 write successive powers of 2 over each digit from
right to left and add up those numbers that are
under a 1.

9. 2.2 Numbering Systems
2.2.2 The Binary Numbering System
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2.2.2.1 Conversions between Binary and Decimal Systems
 To convert from decimal to binary, divide the
number by two. The remainder (which will be either
0 or 1) is the rightmost binary digit.

10. 2.2 Numbering Systems
2.2.3 Hexadecimal Numbering System
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 Hexadecimal numbers have two advantages:
they are very compact (short) and it is simple to
convert them to binary and vice versa. Since the
base of a hexadecimal number is 16, each
hexadecimal digit can represent one of sixteen
values between 0 and 15.

11. 2.2 Numbering Systems
2.2.3 Hexadecimal Numbering System
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2.2.3.1 Decimal to Hexadecimal Conversion

12. 2.2 Numbering Systems
2.2.3 Hexadecimal Numbering System
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2.2.3.2 Binary to Hexadecimal Conversion
 As you can see,
hexadecimal numbers are
compact and easy to read.
 In addition, you can easily
convert between
hexadecimal and binary
using the table.

13. 2.3 Binary Logic
2.3.1 Overview
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 Binary logic is used to build the decision-making
unit in computer systems.
 Decision may consist of a combination of smaller
decisions, each one gives either true (binary value
of 1) or false (binary value of 0) situation.

14. 2.3 Binary Logic
2.3.1 Overview
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 Truth table of AND logical operator

15. 2.3 Binary Logic
2.3.1 Overview
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 Truth table of OR logical operator

16. 2.3 Binary Logic
2.3.1 Overview
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 Truth table of NOT logical operator
1
0

17. 2.3 Binary Logic
2.3.1 Overview
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 First Condition XOR Second Condition
 XOR operator can be explained as following; final
result is true if the first and the second condition
are different.

18. 2.3 Binary Logic
2.3.1 Binary Logical Operations
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The following example illustrates how to apply the
logical operations to the binary numbers.

19. 2.4. Representing Characters
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Each character we wish to use must be assigned a
unique binary code or number to distinguish it from all
other characters.
There are two coding systems:
1- The ASCII code
2- The Unicode.

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ASCII (American Standard Code for Information
Interchange).
We have different characters as:
 Upper-case (A-Z),
 lower-case (a-z),
 numerals (0-9),
 punctuation (, . ; : etc.) and
 control characters (non-printing, e.g. Esc)
2.4. Representing Characters
2.4.1 ASCII Codes (8-bit)

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The following table shows the ASCII table, showing
the codes used for all different characters.
2.4. Representing Characters
2.4.1 ASCII Codes (8-bit)

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Note that upper and lower cases of a letter differ only
in bit 5 making case-conversion easy:
 To change from lower-to-upper: set bit 5 = 0
 To change from upper to lower: set bit 5 = 1
 To change case: invert bit 5
2.4. Representing Characters
2.4.1 ASCII Codes (8-bit)

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 The problem with ASCII codes is that a maximum of 256 (8-
bit) characters can be represented.
 Needed for other languages such as Chinese or Japanese
where there are literally thousands of individual characters
making up the language alphabet.
 Unicode allows more than 65,000 characters to be
represented
 The first 128 Unicode codes correspond to the standard
ASCII codes.
2.4. Representing Characters
2.4.2 Unicode (16-bit)