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Data A 5 4
Practically Keyboard Cable RAM/ CPU Hard disk
Theoretically
I. Introduction
VL VL VH VL VH VL VL VH VL VL VL VL VL VH VL VH VL VL VL VL VL VH VL VL
What is a bit?
The term bit is the contraction of the English words binary digit (which
can be translated as le chiffre binaire in French). It is the simplest unit
used in a number system. This unit can only take two values : 0 and 1.
I. Introduction II. Number Systems III. Informations representation IV. Boolean algebra
I. Introduction
Course Objective
Teach students how to code information. It is about the
knowledge of the relationship between information and its
internal representation in the machine.
Example
The number 5 is represented by the sequence of bits 0000 0101.
The letter A is represented by the sequence of bits 0010 1001.
I. Introduction II. Number Systems III. Informations representation IV. Boolean algebra
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
Introduction
To count in decimal we use ten digits : 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9. When we
have counted up to 9 , we know well that we must go to 10 , 11 …. So, the
number 2021 can be written as follows :
This way of writing numbers is called the positional number system. And
we're talking about base 10.
However, it is possible to imagine other number systems based on a
different integer. For example, we can only count with eight digits from 0
to 7. So when we reach 7 , the 8 does not exist, we move on to 10 , 11 ,...
17 , 20 ... This is base 8.
A Base B : is the number of different symbols used to form numbers in a
so-called base B number system
II. Number Systems
1. Decimal system
Or Base 10 : Consists of using ten digits ( 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 )
Is a weighted system (the digits of a number having weights)
Example :
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
Polynomial Form
(Forme Polynomiale)
Counting in Base 10 :
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
1. Decimal system
By using 1 digit
we can form 10 different numbers =
the smallest number is 0, the largest number is
By using 2 digits
we can form 100 different numbers =
the smallest number is 0, the largest number is
By using n digits
we can form different numbers
the smallest number is 0 , the largest number is
Arithmetic operations in Base 10 :
Addition :
8 6 9 4 7
1 2 5 3 7 1
1 1 I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
1. Decimal system
Division :
2 5 2 1 5
Before proceeding with the division :
120, 5 / 5 = 1205 / 50 120 / 10,5 = 1200 / 105 120, 5 / 5,75 = 1205 / 57,5 = 12050 / 575 I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
1. Decimal system
Arithmetic operations in Base 10 :
2. Binary System
Or by Base 2 : Consists to use 2 digits or bits (0, 1)
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
Is a weighted system (the bits of a number having weights)
Example :
Polynomial Form
(Forme Polynomiale)
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
2. Binary System
Counting in Base 2 :
By using 1 bit
we can form 2 different numbers
the smallest number is 0, the largest number is
By using 2 bits
we can form 4 different numbers
the smallest number is 0 , the largest number is
By using n bits
we can form different numbers
the smallest number is 0, the largest number is
Addition :
1 1 0 0 1 1 1 0
1 I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
2. Binary System
Arithmetic operations in Base 2 :
1 0 1 0 0 0 0 0. 1 0 1 0..
Multiplication :
1 0 1 0
1 1 0 0 1 0 1
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
2. Binary System
Arithmetic operations in Base 2 :
Division :
1 0 1 1 0 1 0
101, 1 / 10 = 1011 / 100 101 / 10,1 = 1010 / 101 110 , 1 / 1,11 = 1101 / 11,1 = 11010 / 111
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
II. Number Systems
2. Binary System
Arithmetic operations in Base 2 :
Before proceeding with the division :
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
Counting in Base 8 :
3. Octal System
II. Number Systems
I. Introduction II. Number Systems Introduction
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Conversion of numbers
- Special binary codes 6.1 BCD code 6.2 Gray code III. Informations representation IV. Boolean algebra
3. Octal System
Counting in Base 8 :
By using 1 digit
we can form 8 different numbers
the smallest number is 0, the largest number is
By using 2 digits
we can form 64 different numbers
the smallest number is 0, the largest number is
By using n digits
we can form different numbers
the smallest number is 0, the largest number is
II. Number Systems
